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Year 2012, Volume: 25 Issue: 1, 89 - 96, 24.01.2012

Abstract

References

  • Abbas, M., Rhodes, B.E., “Fixed and periodic point results in cone metric spaces”, Appl. Math. Lett., 22: 511-515 (2008).
  • Agarwal, R.P., El-Gebeily, M.A., O’Regan, D., “Generalized contractions in partially orderd metric spaces”, Appl. Anal., 87 (1): 109- 116(2008).
  • Altun, I., Durmaz, G., “Some fixed point theorems on ordered cone metric spaces”, Rend. Circ. Mat. Palermo, 58:319-325(2009).
  • Altun, I., Damjanović, B., Djorić, D., “Fixed point and common fixed point theorems on ordered cone metric spaces”, Applied Mathematics Letters, 23: 310-316 (2010).
  • Ćirić, Lj., Cakić, A.N., Rajović, M., Ume, J.S., “Monotone generalized nonlinear contractions in partially metric spaces”, Fixed Point Theory Appl., 11 Article ID 131294(2008).
  • Haung, L.G., Zhang, X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 332: 1468-1476(2007).
  • Janković, S. Golubović, Z., Radenović, S., “Compatible and weakly compatible mappings in cone metric spaces”, Mathematical and Computer Modelling, 52: 1728-1738(2010).
  • Jungck, G., “Compatible mappings and common fixed points”, Int. J. Math. Math. Sci., 771-779 (1986).
  • Jungck, G., Rhoades, B.E., “Fixed point for set valued functions without conyinuity”, Indian J. Pure Appl. Math., 29: 227-238(1998).
  • Karapinar, E., “Couple fixed point theorems for nonlinear contractions in cone metric spaces”, Computers and Mathematics with Applications, doi:10.1016/j.camwa.2010.03.062(2010).
  • Karapinar, E., “Fixed point theorems in cone Banach spaces”, Fixed Point Theory Appl., 9 pages doi:10.1155/2009/609281. Article ID 609281(2009).
  • Karapinar, E., “Coupled fixed point on cone metric spaces”, Gazi University Journal of Science, 24: 51-58(2011).
  • Lakshmikantham, V., Ćirić, Lj., “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces”, Nonlinear Anal., 70 (12): 4341-4349(2009).
  • Ilić, D., Rakočevič, V., “Common fixed points for maps on cone metric space”, J. Math. Anal. Appl., 341: 876-882 (2008).
  • Nashine, H.K., Samet, B., “Fixed point results for mappings satisfying (ψ, φ)-weakly contractive condition in partially ordered metric spaces”, Nonlinear Analysis, doi:10.1016/j.na.2010.11.024(2010).
  • Nieto, J.J., Lopez, R.R., “Existence and uniqeness of fixed point in partially ordered sets and applications to ordinary differential equations”, Acta Math. Sin. (English Ser.), 23 (12): 2205- 2212(2007).
  • Ran, A.C.M., Reuring, M.C.B., “A fixed point theorem in partially ordered sets and some application to matrix equations”, Proc. Amer. Math. Soc., 132:1435-1443(2004).
  • O’Regan, D.A., Sel, P., “Fixed point theorems for generalized contractions in ordered metric spaces”, J. Math. Anal. Appl., 341: 1241-1252 (2008).
  • Rezapour, Sh., Hamlbarani, R., “Some notes on the paper ”Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345: 719-724 (2008).
  • Shatanawi, W., “Partially ordered cone metric spaces and coupled fixed point results”, Computers and Mathematics with Applications, 60: 2508-2515 (2010).
  • Shatanawi, W., “Some common coupled fixed point results in cone metric spaces”, Int. Journal of Math. Analysis, 4: 2381-2388 (2010).
  • Shatanawi, W., Mustafa, Z., “On coupled random fixed point results in partially ordered metric spaces”, accepted in Matematicki Vesnik (2011).
  • Shatanawi, W., Samet, B., “On (ψ, φ)-weakly contractive condition in partially ordered metric spaces”, Computers and Mathematics with Applications, 62: 3204–3214 (2011).
  • Shatanawi, W., “On w-compatible mappings and common coupled coincidence point in cone metric spaces”, Applied Mathematics Letters, doi:10.1016/j.aml.2011.10.037 (2011).
  • Turkoglu, D., Abuloha, M., “Cone metric spaces and fixed point theorems in diametrically contractive mappings”, Acta Math. Sin. (Engl. Ser.), 26 (3): 489-496 (2010).
  • Turkoglu, D., Abuloha, M.T., Abdeljawad,
  • “KKM mappings in cone metric spaces and some fixed point theorems”, Nonlinear Anal. TMA, 72 (1): 348-353 (2010).
  • Wang, C., Zhu, J., Damjanovi´c, B., Hu, L., “Approximating fixed points of contractive type mappings in generalized convex metric spaces”, Appli. Math. Comput., doi:10.1016/j.amc.2009.07.006 (2009).

Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces

Year 2012, Volume: 25 Issue: 1, 89 - 96, 24.01.2012

Abstract

We study some common coincidence and common fixed point theorems for weakly increasing mappings with respect to a self maps on partially ordered cone metric spaces, where the cone is not necessarily normal. Our results generalized several well-known comparable results in the literature.

References

  • Abbas, M., Rhodes, B.E., “Fixed and periodic point results in cone metric spaces”, Appl. Math. Lett., 22: 511-515 (2008).
  • Agarwal, R.P., El-Gebeily, M.A., O’Regan, D., “Generalized contractions in partially orderd metric spaces”, Appl. Anal., 87 (1): 109- 116(2008).
  • Altun, I., Durmaz, G., “Some fixed point theorems on ordered cone metric spaces”, Rend. Circ. Mat. Palermo, 58:319-325(2009).
  • Altun, I., Damjanović, B., Djorić, D., “Fixed point and common fixed point theorems on ordered cone metric spaces”, Applied Mathematics Letters, 23: 310-316 (2010).
  • Ćirić, Lj., Cakić, A.N., Rajović, M., Ume, J.S., “Monotone generalized nonlinear contractions in partially metric spaces”, Fixed Point Theory Appl., 11 Article ID 131294(2008).
  • Haung, L.G., Zhang, X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 332: 1468-1476(2007).
  • Janković, S. Golubović, Z., Radenović, S., “Compatible and weakly compatible mappings in cone metric spaces”, Mathematical and Computer Modelling, 52: 1728-1738(2010).
  • Jungck, G., “Compatible mappings and common fixed points”, Int. J. Math. Math. Sci., 771-779 (1986).
  • Jungck, G., Rhoades, B.E., “Fixed point for set valued functions without conyinuity”, Indian J. Pure Appl. Math., 29: 227-238(1998).
  • Karapinar, E., “Couple fixed point theorems for nonlinear contractions in cone metric spaces”, Computers and Mathematics with Applications, doi:10.1016/j.camwa.2010.03.062(2010).
  • Karapinar, E., “Fixed point theorems in cone Banach spaces”, Fixed Point Theory Appl., 9 pages doi:10.1155/2009/609281. Article ID 609281(2009).
  • Karapinar, E., “Coupled fixed point on cone metric spaces”, Gazi University Journal of Science, 24: 51-58(2011).
  • Lakshmikantham, V., Ćirić, Lj., “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces”, Nonlinear Anal., 70 (12): 4341-4349(2009).
  • Ilić, D., Rakočevič, V., “Common fixed points for maps on cone metric space”, J. Math. Anal. Appl., 341: 876-882 (2008).
  • Nashine, H.K., Samet, B., “Fixed point results for mappings satisfying (ψ, φ)-weakly contractive condition in partially ordered metric spaces”, Nonlinear Analysis, doi:10.1016/j.na.2010.11.024(2010).
  • Nieto, J.J., Lopez, R.R., “Existence and uniqeness of fixed point in partially ordered sets and applications to ordinary differential equations”, Acta Math. Sin. (English Ser.), 23 (12): 2205- 2212(2007).
  • Ran, A.C.M., Reuring, M.C.B., “A fixed point theorem in partially ordered sets and some application to matrix equations”, Proc. Amer. Math. Soc., 132:1435-1443(2004).
  • O’Regan, D.A., Sel, P., “Fixed point theorems for generalized contractions in ordered metric spaces”, J. Math. Anal. Appl., 341: 1241-1252 (2008).
  • Rezapour, Sh., Hamlbarani, R., “Some notes on the paper ”Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345: 719-724 (2008).
  • Shatanawi, W., “Partially ordered cone metric spaces and coupled fixed point results”, Computers and Mathematics with Applications, 60: 2508-2515 (2010).
  • Shatanawi, W., “Some common coupled fixed point results in cone metric spaces”, Int. Journal of Math. Analysis, 4: 2381-2388 (2010).
  • Shatanawi, W., Mustafa, Z., “On coupled random fixed point results in partially ordered metric spaces”, accepted in Matematicki Vesnik (2011).
  • Shatanawi, W., Samet, B., “On (ψ, φ)-weakly contractive condition in partially ordered metric spaces”, Computers and Mathematics with Applications, 62: 3204–3214 (2011).
  • Shatanawi, W., “On w-compatible mappings and common coupled coincidence point in cone metric spaces”, Applied Mathematics Letters, doi:10.1016/j.aml.2011.10.037 (2011).
  • Turkoglu, D., Abuloha, M., “Cone metric spaces and fixed point theorems in diametrically contractive mappings”, Acta Math. Sin. (Engl. Ser.), 26 (3): 489-496 (2010).
  • Turkoglu, D., Abuloha, M.T., Abdeljawad,
  • “KKM mappings in cone metric spaces and some fixed point theorems”, Nonlinear Anal. TMA, 72 (1): 348-353 (2010).
  • Wang, C., Zhu, J., Damjanovi´c, B., Hu, L., “Approximating fixed points of contractive type mappings in generalized convex metric spaces”, Appli. Math. Comput., doi:10.1016/j.amc.2009.07.006 (2009).
There are 28 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Wasfi Shatanawı

Publication Date January 24, 2012
Published in Issue Year 2012 Volume: 25 Issue: 1

Cite

APA Shatanawı, W. (2012). Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces. Gazi University Journal of Science, 25(1), 89-96.
AMA Shatanawı W. Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces. Gazi University Journal of Science. January 2012;25(1):89-96.
Chicago Shatanawı, Wasfi. “Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces”. Gazi University Journal of Science 25, no. 1 (January 2012): 89-96.
EndNote Shatanawı W (January 1, 2012) Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces. Gazi University Journal of Science 25 1 89–96.
IEEE W. Shatanawı, “Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces”, Gazi University Journal of Science, vol. 25, no. 1, pp. 89–96, 2012.
ISNAD Shatanawı, Wasfi. “Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces”. Gazi University Journal of Science 25/1 (January 2012), 89-96.
JAMA Shatanawı W. Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces. Gazi University Journal of Science. 2012;25:89–96.
MLA Shatanawı, Wasfi. “Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces”. Gazi University Journal of Science, vol. 25, no. 1, 2012, pp. 89-96.
Vancouver Shatanawı W. Some Common Coincidence Point Theorems on Weakly Increasing Mappings in Partially Ordered Cone Metric Spaces. Gazi University Journal of Science. 2012;25(1):89-96.