In this paper, we introduce set valued (α,ψ) F-contraction mappings in the setting of a partial metric space. We obtain some common fixed point theorems for a pair of these mappings. These results generalize several recent results existing in the current literature.
Abbas, M., Nazir, T. and Romaguera, S., Fixed point results for generalized cyclic contraction mappings in partial metric spaces, RACSAM- Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matematicas, 106 (2012), 287-297.
Abdeljawad, T., Karapinar, E. and Tas, K., Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett. 24 (2011), 1900-1904.
Al-Rawashdeh, A., Aydi, H., Felhi, Sahmim, A. S. and Shatanawi, W., On common fixed points for α-F-contractions and applications, J. Nonlinear Sci. Appl. 9 (5) (2016), 3445--3458.
Altun, I., Sola, F. and Simsek, H., Generalized contractions on partial metric spaces, Topology Appl. 157 (2010), 2778-2785.
Altun, I. and Romaguera, S., Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point, Applicable Analysis and Discrete Mathematics, 6 (2012), 247-256.
Altun, I., Minak, G. and Dag, H., Multivalued F-Contractions On Complete Metric Space, J. Nonlinear Convex Anal. 16 (2015), 659-666.
Aydi, H., Abbas, M. and Vetro, C., Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology Appl.159 (2012), 3234-3242.
Aydi, H., Abbas, M. andVetro, C., Common Fixed points for multivalued generalized contractions on partial metric spaces, RACSAM - Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matematicas, 108 (2014), 483-501.
Aydi, H., Karapinar, E. andRezapour, Sh., A generalized Meir-Keeler type contraction on partial metric spaces, Abstract and Applied Analysis, Volume 2012, Article ID 287127, 11 pages.
Aydi, H., Barakat, M., Felhi, A. and Işik, H., On φ-contraction type couplings in partial metric spaces, Journal of Mathematical Analysis, 8 (4) (2017), 78--89.
Aydi, H., Karapinar, E. and Kumam, P., A Note on Modified Proof of Caristi's Fixed Point Theorem on Partial Metric Spaces, Journal of Inequalities and Applications 2013:355.
Aydi, H., Karapinar, E. and Yazidi, H., Modified F-contractions via α-admissible mappings and application to integral equations, Filomat, 31 (5) (2017), 1141-1148.
Arshad, M., Hussain, A. and Nazam, M., Some fixed point results for multivalued F-contraction on closed ball, Func. Anal. 2 (2016), 69-80.
Asl, J.H., Rezapour, S. and Shahzad, N., On fixed points of α-ψ-contractive multifunctions, Fixed Point Theory Appl. 2012:212, 2012.
Ćirić, L.J., Samet, B., Aydi, H. and Vetro, C., Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), 2398-2406.
Cosentino, M. and Vetro, P., Fixed point results for F-contractive mappings of Hardy-Rogers-Type, Filomat, 28 (2014), 715-722.
Felhi, A. and Aydi, H., New fixed point results for multi-valued maps via manageable functions and an application on a boundary value problem, U.P.B. Sci. Bull. Series A, 80 (1) (2018), 1-12.
Hussain, A., Nazam, M. and Arshad, M., Connection of Ciric type F-Contraction Involving Fixed Point on Closed Ball, Gazi Univ. J. Sci. 30 (2017), 283-291.
Hussain, A., Ahmad, H.F., Nazam, M. and Arshad, M., New type of multivalued F-contraction involving fixed points on closed ball, J. Math. Computer Sci. 17 (2017), 246-254.
Kumam, P. Vetro, C. and Vetro, F., Fixed points for weak (α-ψ)-contractions in partial metric spaces, Abstract and Applied Analysis, Vol. 2013, 1-9.
Matthews, S.G., Partial Metric Topology, Ann. New York Acad. Sci. 728(1994), 183-197.
Minak, G. Acar, O. and Altun, I., Multivalued pseudo-Picard operators and fixed point results, J. Funct. Spaces Appl. 2013: 827458, 2013.
Nazam, M., Arshad, M. and Park, C., Fixed point theorems for improved α-Geraghty contractions in partial metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 4436-4449.
Samet, B., Vetro, C. and Vetro, P., Fixed point theorems for (α-ψ) contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.
Wardowski, D., Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. (2012), Article ID 94.
Abbas, M., Nazir, T. and Romaguera, S., Fixed point results for generalized cyclic contraction mappings in partial metric spaces, RACSAM- Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matematicas, 106 (2012), 287-297.
Abdeljawad, T., Karapinar, E. and Tas, K., Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett. 24 (2011), 1900-1904.
Al-Rawashdeh, A., Aydi, H., Felhi, Sahmim, A. S. and Shatanawi, W., On common fixed points for α-F-contractions and applications, J. Nonlinear Sci. Appl. 9 (5) (2016), 3445--3458.
Altun, I., Sola, F. and Simsek, H., Generalized contractions on partial metric spaces, Topology Appl. 157 (2010), 2778-2785.
Altun, I. and Romaguera, S., Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point, Applicable Analysis and Discrete Mathematics, 6 (2012), 247-256.
Altun, I., Minak, G. and Dag, H., Multivalued F-Contractions On Complete Metric Space, J. Nonlinear Convex Anal. 16 (2015), 659-666.
Aydi, H., Abbas, M. and Vetro, C., Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology Appl.159 (2012), 3234-3242.
Aydi, H., Abbas, M. andVetro, C., Common Fixed points for multivalued generalized contractions on partial metric spaces, RACSAM - Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matematicas, 108 (2014), 483-501.
Aydi, H., Karapinar, E. andRezapour, Sh., A generalized Meir-Keeler type contraction on partial metric spaces, Abstract and Applied Analysis, Volume 2012, Article ID 287127, 11 pages.
Aydi, H., Barakat, M., Felhi, A. and Işik, H., On φ-contraction type couplings in partial metric spaces, Journal of Mathematical Analysis, 8 (4) (2017), 78--89.
Aydi, H., Karapinar, E. and Kumam, P., A Note on Modified Proof of Caristi's Fixed Point Theorem on Partial Metric Spaces, Journal of Inequalities and Applications 2013:355.
Aydi, H., Karapinar, E. and Yazidi, H., Modified F-contractions via α-admissible mappings and application to integral equations, Filomat, 31 (5) (2017), 1141-1148.
Arshad, M., Hussain, A. and Nazam, M., Some fixed point results for multivalued F-contraction on closed ball, Func. Anal. 2 (2016), 69-80.
Asl, J.H., Rezapour, S. and Shahzad, N., On fixed points of α-ψ-contractive multifunctions, Fixed Point Theory Appl. 2012:212, 2012.
Ćirić, L.J., Samet, B., Aydi, H. and Vetro, C., Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), 2398-2406.
Cosentino, M. and Vetro, P., Fixed point results for F-contractive mappings of Hardy-Rogers-Type, Filomat, 28 (2014), 715-722.
Felhi, A. and Aydi, H., New fixed point results for multi-valued maps via manageable functions and an application on a boundary value problem, U.P.B. Sci. Bull. Series A, 80 (1) (2018), 1-12.
Hussain, A., Nazam, M. and Arshad, M., Connection of Ciric type F-Contraction Involving Fixed Point on Closed Ball, Gazi Univ. J. Sci. 30 (2017), 283-291.
Hussain, A., Ahmad, H.F., Nazam, M. and Arshad, M., New type of multivalued F-contraction involving fixed points on closed ball, J. Math. Computer Sci. 17 (2017), 246-254.
Kumam, P. Vetro, C. and Vetro, F., Fixed points for weak (α-ψ)-contractions in partial metric spaces, Abstract and Applied Analysis, Vol. 2013, 1-9.
Matthews, S.G., Partial Metric Topology, Ann. New York Acad. Sci. 728(1994), 183-197.
Minak, G. Acar, O. and Altun, I., Multivalued pseudo-Picard operators and fixed point results, J. Funct. Spaces Appl. 2013: 827458, 2013.
Nazam, M., Arshad, M. and Park, C., Fixed point theorems for improved α-Geraghty contractions in partial metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 4436-4449.
Samet, B., Vetro, C. and Vetro, P., Fixed point theorems for (α-ψ) contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.
Wardowski, D., Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. (2012), Article ID 94.
Nazam, M., Aydi, H., & Arshad, M. (2019). On some problems regarding set valued (α,ψ)-F-contractions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1240-1255. https://doi.org/10.31801/cfsuasmas.516595
AMA
Nazam M, Aydi H, Arshad M. On some problems regarding set valued (α,ψ)-F-contractions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1240-1255. doi:10.31801/cfsuasmas.516595
Chicago
Nazam, Muhammad, Hassen Aydi, and Muhammad Arshad. “On Some Problems Regarding Set Valued (α,ψ)-F-Contractions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1240-55. https://doi.org/10.31801/cfsuasmas.516595.
EndNote
Nazam M, Aydi H, Arshad M (August 1, 2019) On some problems regarding set valued (α,ψ)-F-contractions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1240–1255.
IEEE
M. Nazam, H. Aydi, and M. Arshad, “On some problems regarding set valued (α,ψ)-F-contractions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1240–1255, 2019, doi: 10.31801/cfsuasmas.516595.
ISNAD
Nazam, Muhammad et al. “On Some Problems Regarding Set Valued (α,ψ)-F-Contractions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1240-1255. https://doi.org/10.31801/cfsuasmas.516595.
JAMA
Nazam M, Aydi H, Arshad M. On some problems regarding set valued (α,ψ)-F-contractions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1240–1255.
MLA
Nazam, Muhammad et al. “On Some Problems Regarding Set Valued (α,ψ)-F-Contractions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1240-55, doi:10.31801/cfsuasmas.516595.
Vancouver
Nazam M, Aydi H, Arshad M. On some problems regarding set valued (α,ψ)-F-contractions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1240-55.