Coupled Coincidence Points for F-Contractive Type Mappings in Partially Ordered Metric Spaces

Time:2019-11-15

SONG Jiping School of Mathematics and Information Science, Leshan Normal University, Leshan 614000, Sichuan, China

Abstract:

In this article, some coupled coincidence point results for two mappings g: X → X and G: X × X → X satisfying F-contractive type conditions are obtained, and some coupled fixed point results are derived in partially ordered metric spaces. A sufficient condition for uniqueness of coupled point of coincidence are established for F type contraction, and a coupled common fixed point theorem is obtained. Some examples are given to support our results.

[1] Bhaskar T G, Laksmikantham V. Fixed point theorems in partially ordered metric spaces and applications [J]. Nonlinear Anal, 2006, 65(7): 1379-1393.
[2] Laksmikantham V, Ćirić L. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces [J]. Nonlinear Anal Theory Methods Appl, 2009, 70(12): 4341- 4349.
[3] Harjani J, López B , Sadarangani K. Fixed point theorems for mixed monotone operators and applications to integral equations [J]. Nonlinear Anal, 2011, 74(5): 1749-1760.
[4] Luong N V, Thuan N X. Coupled fixed points in partially ordered metric spaces and application [J]. Nonlinear Anal, 2011, 74: 983-992.
[5] Nashine H K, Samet B , Vetro C. Coupled coincidence points for compatible mappings satisfying mixed monotone property [J]. J Nonlinear Sci Appl, 2012, 5(2): 104-114.
[6] Choudhury B S, Kundu A. A coupled coincidence point result in partially ordered metric spaces for compatible mappings [J]. Nonlinear Anal, 2010, 73(8): 2524-2531.
[7] Nashine H K, Shatanawi W. Coupled common fixed point theorems for pair of commuting mappings in partially ordered complete metric spaces [J]. Comput Amer Math Appl, 2011, 62(4): 1984-1993.
[8] Kaushik P, Kumar S , Kumam P. Coupled coincidence point theorems for contractive type mappings in partially ordered metric spaces [J]. Fixed Point Theory Appl, 2013, 2013(1): 325.
[9] Berinde V. Coupled coincidence point theorems for mixed monotone nonlinear operators [J]. Comput Math Appl, 2012, 64(6): 1770-1777.
[10] Abbas M, Khan M A, Radenovic S. Common coupled fixed point theorem in cone metric space for w-compatible map-pings [J]. Appl Math Comput, 2010, 217(1): 195-202 .
[11] Agarwal R P, Sintunavarat W, Kumam P. Coupled coinci-dence point and common coupled fixed point theorems lacking the mixed monotone property [J]. Fixed Point Theory and Applications, 2013, 2013(1): 22.
[12] Wardowski D. Fixed points of a new type of contractive mappings in complete metric spaces [J]. Fixed Point and Applications, 2012, 2012(1): 94.
[13] Wardowski D, Van Dung N. Fixed points of F-weak contrac-tions on complete metric spaces [J]. Demonstratio Math, 2014, 47(1): 146-155.
[14] Sgroi M, Vetro C. Multi-valued F-contractions and the solu-tion of certain functional and integral equations [J]. Filomat , 2013, 27(7): 1259-1268. DOI : 10.2298/FIL130 7259S.
[15] Batra R, Vashistha S, Kumar R. A coincidence point theorem for F-contractions on metric spaces equipped with an altered distance[J]. J Math Comput Sci, 2014, 4(5): 826-833.
[16] Batra R, Vashistha S, Kumar R. Coincidence point theorem for a new type of contraction on metric spaces [J]. Int Journal of Math Analysis, 2014, 8(27): 1315-1320.
[17] Dhananjay G, Mujahid A, Deepesh Kumar P, et al. Fixed points of F-contractive mappings with an application to nonlinear fractional differential equation [J]. Acta Math Sci, 2016, 36(3): 957-970.