Coincidence Point Theorems on $b$-Metric Spaces via $C_{F}$-Simulation Functions

Year 2019, Volume: 2 Issue: 4, 244 - 250, 29.12.2019

Reyhan Özçelik , Emrah Evren Kara

https://doi.org/10.33434/cams.567268

Abstract

In this paper, we investigate the existence and uniqueness of the coincidence points with the $C_{F}$-simulation function for  two nonlinear operators on the $b$-metric space. Our results  improve and generalize some of the results available in the literature.

Keywords

b-metric space, Fixed point, Simulation function

References

• [1] S. Banach, Sur les operations dans les ensembles abstraits et leur application auxequations integrales, Fund. Math., 3 (1922), 133-181.
• [2] J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72(3-4) (2010), 1188-1197.
• [3] J. J. Nieto, R. Rodr´ıguez-L´opez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23(12) (2007), 2205-2212.
• [4] F. Khojasteh, S. Shukla, S.Radenovi´c, A new approach to the study of fixed point theory for simulation functions, Filomat, 29(6) (2015), 1189-1194.
• [5] A. F. Rold´an-L´opez-de-Hierro, E. Karapınar, C. Rold´an-L´opez-de-Hierro, J. Mart´ınez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), 345-355.
• [6] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Func. An. (Gos. Ped. Inst. Unianowsk), 30 (1989), 26-37.
• [7] G. V. R. Babu, P. D. Sailaja, A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai J. Math., 9(1) (2012), 1-10.
• [8] J. R. Roshan, V. Parvaneh, Z. Kadelburg, Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci., 7(4) (2014), 229-245.
• [9] G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227-238.
• [10] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83(4) (1976), 261-263.
• [11] A. H. Ansari, Note on “a-admissible mappings and related fixed point theorems”, In the 2nd Regional Conference on Mathematics and Applications, Payame Noor University, (2014), 373-376.