A Common Fixed Point Theorem for Nonlinear Quasi-Contractions on $b$-Metric Spaces with Application in Integral Equations

Abstract

In this paper, we present a common fixed point result for a pair of mappings defined on a b-metric space, which satisfies quasi-contractive inequality with nonlinear comparison functions. An application in solving a class of integral equations will support our results.

The Results on Coincidence and Common Fixed Points for a New Type Multivalued Mappings in b-Metric Spaces

“…In this article, we give the results on the existence of a point of coincidence and a common strict fixed point for a hybrid pair of single-valued and multivalued mappings defined in b-metric spaces, which satisfy quasi-contractive inequality with nonlinear comparison function. Our results extend and generalize the results presented in [1,[4][5][6][11][12][13][14]. Finally, we give an application of our results in the topological theory of set-valued dynamical systems.…”

“…A common fixed-point result for single-valued nonlinear quasi-contractions was presented by Z. D. Mitrović et al [14].…”

“…A. Ivanov [5], I. Arandelović, M. Rajović and V. Kilibarda [6] and M. Bessenyei [7], common fixed-point results of K. M. Das, K. V. Naik [9] and C. Di Bari and P. Vetro [10]. Please note that contractive condition (1) was defined earlier by several authors; see for example [14].…”