A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function

Selma Gülyaz; Erdal Karapınar

A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function

Year 2013, Volume: 42 Issue: 4, 347 - 357, 01.04.2013

Abstract

In this manuscript, we discuss the existence of coupled fixed points inthe context of partially ordered metric spaces through implicit relationsfor mappings F : X× X → X such that F has the mixed monotoneproperty. Our main theorem improves and extends various results inthe literature. We also state an example to illustrate our work.

Keywords

Coupled fixed point; Mixed monotone property; Implicit relation; Orderedpartial metric space2000

References

Abbas, M., Sintunavarat, W. and Kumam,P. Coupled xed point in partially or- dered Gmetric spaces, Fixed Point Theory and Applications 2012, 2012:31.
Abbas,M., Nazir, T. and Romaguera,S. Fixed point results for generalized cyclic contraction mappings in partial metric spaces, Revista de la Real Academia de Ciencias Exactas, (in press), doi:10.1007/s13398–011-0051-5.
Abdeljawad, T. Fixed Points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling 54(11-12), 2923–2927, 2011.
Abdeljawad,T., Karapınar, E. and Ta¸s, K. Existence and uniqueness of common fixed point on partial metric spaces, Appl. Math. Lett. 24, 1894–1899, 2011.
Abdeljawad,T., Karapınar, E. and Ta¸s, K. A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl. 63 (3), 716–719, 2012.
Altun, I. and Turkoglu, D. Some fixed point theorems for weakly compatible multivalued mappings satisfying an implicit relation, Filomat 22, 13–23, 2008.
Altun, I., Sola, F. and Simsek,H. Generalized contractions on partial metric spaces, Topology and Appl. 157 (18), 2778–2785, 2010.
Aydi, H., Vetro, C., Sintunavarat,W. and Kumam,P. Coincidence and xed points for contractions and cyclical contractions in partial metric spaces, Fixed Point Theory and Applications, (to appear). Aydi, H., Karapınar, E. and Shatanawi, W. Coupled fixed point results for (ψ, ϕ)-weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl. 62(12), 4449– 4460, 2011.
Gnana Bhaskar,T. and Lakshmikantham, V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 , 1379–1393, 2006.
Berinde, V. Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 74, 7347–7355, 2011.
Berinde, V. Coupled fixed point theorems for φ -contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 75, 3218–3228, 2012.
Choudhury, B.S. and Kundu,A. A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Analysis 73, 2524–2531, 2010.
Choudhury, B.S., Metiya,N. and Kundu, A. Coupled coincidence point theorems in ordered metric spaces. Ann. Univ. Ferrara 57, 1–16, 2011.
Ciric, L., Cakic,N., Rajovic, M. and Ume, J.S. Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2008, Art. ID 131294, 2008. Chi, K.P., Karapınar, E. and Thanh, T. D. A generalized contraction principle in partial metric spaces, Math. Comput. Modelling 55 (5–6), 1673–1681, 2012.
´ Ciri´ c, Lj. On contraction type mappings, Math. Balkanica 1, 52–57, 1971.
´ Ciri´ c, Lj., Samet, B., Aydi, H. and Vetro, C. Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 18 (6), 2398–2406, 2011. Djoudi, A. and Aliouche, A. A general common fixed point theorem for reciprocally continuous mappings satisfying an implicit relation, The Austral. J. Math. Anal. Appl. 3, 1–7, 200
Fr´ echet, M. Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo 22 , 1—74, 190 Harjani, J., Lopez, B. and Sadarangani, K. Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 , 1749–1760, 2011.
Hung,N.M., Karapinar,E. and Luong, N.V. Coupled coincidence point theorem in partially ordered metric spaces via implicit relation, Abstract and Applied Analysis 2012, Art. ID 796964, 2012.
Heckmann, R. Approximation of metric spaces by partial metric spaces, Applied Categorical Structures 7, 71—83, 1999.
Ili´ c, D., Pavlovi´ c, V. and Rako¸cevi´ c, V. Some new extensions of Banach’s contraction principle to partial metric space, Appl. Math. Lett. 24(8), 1326—1330, 2011.
Ili´ c, D., Pavlovi´ c, V. and Rako¸cevi´ c, V. Extensions of the Zamfirescu theorem to partial metric spaces Original Research Article, Math. Comput. Modelling 55(3–4), 801–809, 2012. D.Guo, V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications. Nonlinear Anal., 11 (1987) 623–632.
Jachymski, J. Equivalent Conditions and the Meir-Keeler Type Theorems, J.Math. Anal. Appl. 194 (1), 293–303, 1995.
Kadelburg, Z. and Radenovi´ c, S. Meir–Keeler-type conditions in abstract metric spaces, Appl.Math. Lett. 24 (8), 1411–1414, 2011.
Karapınar, E. Coupled fixed point theorems for nonlinear contractions in cone metric spaces, Computers and Mathematics with Applications 59, 3656–3668, 2010.
Karapınar, E. and Erhan, I. M. Fixed Point Theorems for Operators on Partial Metric Spaces, Appl. Math. Lett. 24, 1900–1904, 2011.
Karapınar, E. Generalizations of Caristi Kirk’s Theorem on Partial Metric Spaces, Fixed Point Theory Appl. 2011(4), doi:10.1186/1687-1812-2011-4, 2011.
Karapınar, E. and Yuksel, U. Some common fixed point theorems in partial metric spaces, Journal of Applied Mathematics 2011, Art. ID 263621, 2011.
Karapınar, E. A note on common fixed point theorems in partial metric spaces, Miskolc Mathematical Notes 12 (2), 185–191, 2011.
Karapınar, E. Couple Fixed Point on Cone Metric Spaces , Gazi University Journal of Science 24, 51–58, 2011.
Karapınar, E. Weak φ-contraction on partial metric spaces, J. Comput. Anal. Appl. 14 (2), 206–210, 2012.
Karapınar, E., Erhan, ˙I.M. and Ulus, A.Y. Fixed Point Theorem for Cyclic Maps on Partial Metric Spaces, Appl. Math. Inf. Sci. 6 (1), 239-244, 2012.
Karapınar, E., Shobkolaei, N., Sedghi, S. and Vaezpour, S.M. A common fixed point theorem for cyclic operators on partial metric spaces, FILOMAT 26(2), 407-414, 2012.
Karapınar, E., Nguyen Van Luong, Nguyen Xuan Thuan, Trinh Thi Hai, Coupled coincidence points for mixed monotone operators in partially ordered metric spaces, Arabian Journal of Mathematics, 1(2012),no: 3, 329–339.
Kopperman, R. D., Matthews, S. G. and Pajoohesh, H. What do partial metrics represent?, (Notes distributed at the 19th Summer Conference on Topology and its Applications, University of CapeTown, 2004).
K¨ unzi, H. P. A., Pajoohesh, H. and Schellekens, M.P. Partial quasi-metrics, Theoretical Computer Science 365(3), 237–246, 2006.
Lakshmikantham, V. and Ciric, L. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70, 4341–4349, 2009.
Luong, N. V. and Thuan, N. X. Coupled fixed point theorems in partially ordered metric spaces, Bull. Math. Anal. Appl. 2 (4), 16–24, 2010.
Luong, N. V. and Thuan, N. X. Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74, 983–992, 2011.
Luong, N. V. and Thuan, N. X. Coupled fixed point theorems for mixed monotone mappings and an application to integral equations, Compt. Math. Appl. 62, 4238–4248, 2011.
Luong, N. V. and Thuan, N. X. Coupled points in ordered generalized metric spaces and application to integro-differential equations, (Submitted). Matthews, S. G. Partial metric topology, in: Procedings 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728, 183–197, 1994.
Meir, A. and Keeler, E. A theorem on contraction mapping, J. Math. Anal. Appl. 28, 326– 329, 1969.
Nashine, H. K., Kadelburg, Z. and Radenovi´ c, S. Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces, Math. Comput. Modelling, (in press), doi:10.1016/j.mcm.2011.12.019.
Nieto,J.J. and Rodriguez-Lopez, R. Contractive mapping theorems in partially ordered sets and applications to ordinary differential equation, Order, 22(3), 223–239, 2005.
Oltra, S. and Valero, O. Banach’s fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste 36(1-2), 17–26, 2004.
O’Neill, S. J.Two topologies are better than one, (Tech. report, University of Warwick, 1995). [52] Paesano, D. and Vetro, P.Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology and its Applications 159 (3), 911–920, 2012.
Popa, V. A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonstratio Math. 33, 159–164, 2000.
Popa, V. A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation, Filomat 19, 45–51, 2005.
Ran, A.C.M. and Reurings, M.C.B. A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 , 1435–1443, 2004.
Rhoades, B.E. andJungck, G. Fixed points for set valued functions without continuity, Indian J.pure and Appl.Math. 29(3), 227-238, 1998.
Romaguera, S. and Schellekens, M. Duality and quasi-normability for complexity spaces, Appl. General Topology 3, 91–112, 2002.
Romaguera, S. and Schellekens, M. Partial metric monoids and semivaluation spaces, Topology and Its Applications, 153 (5-6), 948–962, 2005.
Romaguera, S. and Valero, O. A quantitative computational model for complete partial metric spaces via formal balls, Mathematical Structures in Computer Science 19 (3), 541– 563, 2009.
Romaguera, S. A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory and Applications 2010, Art. ID 493298, 2010.
Romaguera, S. Matkowski’s type theorems for generalized contractions on (ordered) partial metric spaces, Appl. General Topology 12 (2), 213–220, 2011.
Romaguera, S. Fixed point theorems for generalized contractions on partial metric spaces, Topology Appl. 159, 194-199, 2012.
Samet, B. Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72, 4508–4517, 2010.
Samet, B., Rajovi´ c, M., Lazovi´ c, R. and Stoiljkovi´ c, R. Common fixed point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl. 2011, 2011:7
Schellekens, M. P. A characterization of partial metrizability: domains are quantifiable, Theoretical Computer Science 305 (1–3), 409–432, 2003
Schellekens, M. P. The correspondence between partial metrics and semivaluations, Theoretical Computer Science 315(1), 135–149, 2004.
Shatanawi, W., Samet, B. and Abbas, M. Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling 55 (3-4), 680–687
Shobkolaei,N., Vaezpour, S.M. and Sedghi, S. A common fixed point theorem on ordered partial metric spaces, J. Basic. Appl. Sci. Res. 1 (12), 3433–3439, 2011.
Sintunavarat, W., Cho, Y. J. and Kumam, P. Coupled coincidence point theo- rems for contractions without commutative condition in intuitionistic fuzzy normed spaces, Fixed Point Theory and Applications 2011, 2011:81.

A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function

Year 2013, Volume: 42 Issue: 4, 347 - 357, 01.04.2013

Selma Gülyaz Erdal Karapınar

Abstract

Keywords

References

Abbas, M., Sintunavarat, W. and Kumam,P. Coupled xed point in partially or- dered Gmetric spaces, Fixed Point Theory and Applications 2012, 2012:31.
Abbas,M., Nazir, T. and Romaguera,S. Fixed point results for generalized cyclic contraction mappings in partial metric spaces, Revista de la Real Academia de Ciencias Exactas, (in press), doi:10.1007/s13398–011-0051-5.
Abdeljawad, T. Fixed Points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling 54(11-12), 2923–2927, 2011.
Abdeljawad,T., Karapınar, E. and Ta¸s, K. Existence and uniqueness of common fixed point on partial metric spaces, Appl. Math. Lett. 24, 1894–1899, 2011.
Abdeljawad,T., Karapınar, E. and Ta¸s, K. A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl. 63 (3), 716–719, 2012.
Altun, I. and Turkoglu, D. Some fixed point theorems for weakly compatible multivalued mappings satisfying an implicit relation, Filomat 22, 13–23, 2008.
Altun, I., Sola, F. and Simsek,H. Generalized contractions on partial metric spaces, Topology and Appl. 157 (18), 2778–2785, 2010.
Aydi, H., Vetro, C., Sintunavarat,W. and Kumam,P. Coincidence and xed points for contractions and cyclical contractions in partial metric spaces, Fixed Point Theory and Applications, (to appear). Aydi, H., Karapınar, E. and Shatanawi, W. Coupled fixed point results for (ψ, ϕ)-weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl. 62(12), 4449– 4460, 2011.
Gnana Bhaskar,T. and Lakshmikantham, V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 , 1379–1393, 2006.
Berinde, V. Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 74, 7347–7355, 2011.
Berinde, V. Coupled fixed point theorems for φ -contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 75, 3218–3228, 2012.
Choudhury, B.S. and Kundu,A. A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Analysis 73, 2524–2531, 2010.
Choudhury, B.S., Metiya,N. and Kundu, A. Coupled coincidence point theorems in ordered metric spaces. Ann. Univ. Ferrara 57, 1–16, 2011.
Ciric, L., Cakic,N., Rajovic, M. and Ume, J.S. Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2008, Art. ID 131294, 2008. Chi, K.P., Karapınar, E. and Thanh, T. D. A generalized contraction principle in partial metric spaces, Math. Comput. Modelling 55 (5–6), 1673–1681, 2012.
´ Ciri´ c, Lj. On contraction type mappings, Math. Balkanica 1, 52–57, 1971.
´ Ciri´ c, Lj., Samet, B., Aydi, H. and Vetro, C. Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 18 (6), 2398–2406, 2011. Djoudi, A. and Aliouche, A. A general common fixed point theorem for reciprocally continuous mappings satisfying an implicit relation, The Austral. J. Math. Anal. Appl. 3, 1–7, 200
Fr´ echet, M. Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo 22 , 1—74, 190 Harjani, J., Lopez, B. and Sadarangani, K. Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 , 1749–1760, 2011.
Hung,N.M., Karapinar,E. and Luong, N.V. Coupled coincidence point theorem in partially ordered metric spaces via implicit relation, Abstract and Applied Analysis 2012, Art. ID 796964, 2012.
Heckmann, R. Approximation of metric spaces by partial metric spaces, Applied Categorical Structures 7, 71—83, 1999.
Ili´ c, D., Pavlovi´ c, V. and Rako¸cevi´ c, V. Some new extensions of Banach’s contraction principle to partial metric space, Appl. Math. Lett. 24(8), 1326—1330, 2011.
Ili´ c, D., Pavlovi´ c, V. and Rako¸cevi´ c, V. Extensions of the Zamfirescu theorem to partial metric spaces Original Research Article, Math. Comput. Modelling 55(3–4), 801–809, 2012. D.Guo, V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications. Nonlinear Anal., 11 (1987) 623–632.
Jachymski, J. Equivalent Conditions and the Meir-Keeler Type Theorems, J.Math. Anal. Appl. 194 (1), 293–303, 1995.
Kadelburg, Z. and Radenovi´ c, S. Meir–Keeler-type conditions in abstract metric spaces, Appl.Math. Lett. 24 (8), 1411–1414, 2011.
Karapınar, E. Coupled fixed point theorems for nonlinear contractions in cone metric spaces, Computers and Mathematics with Applications 59, 3656–3668, 2010.
Karapınar, E. and Erhan, I. M. Fixed Point Theorems for Operators on Partial Metric Spaces, Appl. Math. Lett. 24, 1900–1904, 2011.
Karapınar, E. Generalizations of Caristi Kirk’s Theorem on Partial Metric Spaces, Fixed Point Theory Appl. 2011(4), doi:10.1186/1687-1812-2011-4, 2011.
Karapınar, E. and Yuksel, U. Some common fixed point theorems in partial metric spaces, Journal of Applied Mathematics 2011, Art. ID 263621, 2011.
Karapınar, E. A note on common fixed point theorems in partial metric spaces, Miskolc Mathematical Notes 12 (2), 185–191, 2011.
Karapınar, E. Couple Fixed Point on Cone Metric Spaces , Gazi University Journal of Science 24, 51–58, 2011.
Karapınar, E. Weak φ-contraction on partial metric spaces, J. Comput. Anal. Appl. 14 (2), 206–210, 2012.
Karapınar, E., Erhan, ˙I.M. and Ulus, A.Y. Fixed Point Theorem for Cyclic Maps on Partial Metric Spaces, Appl. Math. Inf. Sci. 6 (1), 239-244, 2012.
Karapınar, E., Shobkolaei, N., Sedghi, S. and Vaezpour, S.M. A common fixed point theorem for cyclic operators on partial metric spaces, FILOMAT 26(2), 407-414, 2012.
Karapınar, E., Nguyen Van Luong, Nguyen Xuan Thuan, Trinh Thi Hai, Coupled coincidence points for mixed monotone operators in partially ordered metric spaces, Arabian Journal of Mathematics, 1(2012),no: 3, 329–339.
Kopperman, R. D., Matthews, S. G. and Pajoohesh, H. What do partial metrics represent?, (Notes distributed at the 19th Summer Conference on Topology and its Applications, University of CapeTown, 2004).
K¨ unzi, H. P. A., Pajoohesh, H. and Schellekens, M.P. Partial quasi-metrics, Theoretical Computer Science 365(3), 237–246, 2006.
Lakshmikantham, V. and Ciric, L. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70, 4341–4349, 2009.
Luong, N. V. and Thuan, N. X. Coupled fixed point theorems in partially ordered metric spaces, Bull. Math. Anal. Appl. 2 (4), 16–24, 2010.
Luong, N. V. and Thuan, N. X. Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74, 983–992, 2011.
Luong, N. V. and Thuan, N. X. Coupled fixed point theorems for mixed monotone mappings and an application to integral equations, Compt. Math. Appl. 62, 4238–4248, 2011.
Luong, N. V. and Thuan, N. X. Coupled points in ordered generalized metric spaces and application to integro-differential equations, (Submitted). Matthews, S. G. Partial metric topology, in: Procedings 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728, 183–197, 1994.
Meir, A. and Keeler, E. A theorem on contraction mapping, J. Math. Anal. Appl. 28, 326– 329, 1969.
Nashine, H. K., Kadelburg, Z. and Radenovi´ c, S. Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces, Math. Comput. Modelling, (in press), doi:10.1016/j.mcm.2011.12.019.
Nieto,J.J. and Rodriguez-Lopez, R. Contractive mapping theorems in partially ordered sets and applications to ordinary differential equation, Order, 22(3), 223–239, 2005.
Oltra, S. and Valero, O. Banach’s fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste 36(1-2), 17–26, 2004.
O’Neill, S. J.Two topologies are better than one, (Tech. report, University of Warwick, 1995). [52] Paesano, D. and Vetro, P.Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology and its Applications 159 (3), 911–920, 2012.
Popa, V. A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonstratio Math. 33, 159–164, 2000.
Popa, V. A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation, Filomat 19, 45–51, 2005.
Ran, A.C.M. and Reurings, M.C.B. A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 , 1435–1443, 2004.
Rhoades, B.E. andJungck, G. Fixed points for set valued functions without continuity, Indian J.pure and Appl.Math. 29(3), 227-238, 1998.
Romaguera, S. and Schellekens, M. Duality and quasi-normability for complexity spaces, Appl. General Topology 3, 91–112, 2002.
Romaguera, S. and Schellekens, M. Partial metric monoids and semivaluation spaces, Topology and Its Applications, 153 (5-6), 948–962, 2005.
Romaguera, S. and Valero, O. A quantitative computational model for complete partial metric spaces via formal balls, Mathematical Structures in Computer Science 19 (3), 541– 563, 2009.
Romaguera, S. A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory and Applications 2010, Art. ID 493298, 2010.
Romaguera, S. Matkowski’s type theorems for generalized contractions on (ordered) partial metric spaces, Appl. General Topology 12 (2), 213–220, 2011.
Romaguera, S. Fixed point theorems for generalized contractions on partial metric spaces, Topology Appl. 159, 194-199, 2012.
Samet, B. Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72, 4508–4517, 2010.
Samet, B., Rajovi´ c, M., Lazovi´ c, R. and Stoiljkovi´ c, R. Common fixed point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl. 2011, 2011:7
Schellekens, M. P. A characterization of partial metrizability: domains are quantifiable, Theoretical Computer Science 305 (1–3), 409–432, 2003
Schellekens, M. P. The correspondence between partial metrics and semivaluations, Theoretical Computer Science 315(1), 135–149, 2004.
Shatanawi, W., Samet, B. and Abbas, M. Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling 55 (3-4), 680–687
Shobkolaei,N., Vaezpour, S.M. and Sedghi, S. A common fixed point theorem on ordered partial metric spaces, J. Basic. Appl. Sci. Res. 1 (12), 3433–3439, 2011.
Sintunavarat, W., Cho, Y. J. and Kumam, P. Coupled coincidence point theo- rems for contractions without commutative condition in intuitionistic fuzzy normed spaces, Fixed Point Theory and Applications 2011, 2011:81.

There are 62 citations in total.

Details

Primary Language	Turkish
Journal Section	Mathematics
Authors	Selma Gülyaz This is me Erdal Karapınar This is me
Publication Date	April 1, 2013
Published in Issue	Year 2013 Volume: 42 Issue: 4

Cite

APA	Gülyaz, S., & Karapınar, E. (2013). A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function. Hacettepe Journal of Mathematics and Statistics, 42(4), 347-357.
AMA	Gülyaz S, Karapınar E. A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function. Hacettepe Journal of Mathematics and Statistics. April 2013;42(4):347-357.
Chicago	Gülyaz, Selma, and Erdal Karapınar. “A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function”. Hacettepe Journal of Mathematics and Statistics 42, no. 4 (April 2013): 347-57.
EndNote	Gülyaz S, Karapınar E (April 1, 2013) A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function. Hacettepe Journal of Mathematics and Statistics 42 4 347–357.
IEEE	S. Gülyaz and E. Karapınar, “A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 4, pp. 347–357, 2013.
ISNAD	Gülyaz, Selma - Karapınar, Erdal. “A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function”. Hacettepe Journal of Mathematics and Statistics 42/4 (April 2013), 347-357.
JAMA	Gülyaz S, Karapınar E. A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function. Hacettepe Journal of Mathematics and Statistics. 2013;42:347–357.
MLA	Gülyaz, Selma and Erdal Karapınar. “A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 4, 2013, pp. 347-5.
Vancouver	Gülyaz S, Karapınar E. A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function. Hacettepe Journal of Mathematics and Statistics. 2013;42(4):347-5.

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