Fixed Point of Generalized Weak Contraction in $b$-Metric Spaces

Abstract

In this manuscript, a class of generalized ψ , α , β -weak contraction is introduced and some fixed point theorems in the framework of b -metric space are proved. The result presented in this paper generalizes some of the earlier results in the existing literature. Further, some examples and an application are provided to illustrate our main result.

On Existence of Fixed Points for Multivalued Generalized wb‐Contractive Mappings and Applications

“…Recently, fixed-point theory for metric-type spaces studied and developed by many authors, for example, see [5,7,28,32] and references therein.…”

“…It has been observed that the class of metric type spaces is effectively larger than the class of metric spaces [1]. In literature, a number of metric fixed-point results for single-valued and multivalued mappings have been shown; see, for example, [4][5][6][7][8][9][10][11] and references therein.…”

GENERALIZED WARDOWSKI TYPE CONTRACTIVE MAPPINGS IN b -METRIC SPACE WITH APPLICATIONS

“…Recently, Kamran et al [12] published some fixed point results for selfmappings defined on extended b-metric space, which is a generalization of b-metric space. Since then, various writers have demonstrated fixed point findings for single and multivalued operators in b-metric spaces (see [1,6,7,8,9,10,17,18]). All of these uses made us want to talk about the idea of b-metric space.…”

On Fixed-Point Results of Generalized Contractions

“…Its results are supportive tools for other fields to solve many problems. Many researchers have put their efforts in obtaining these results; for further study, see [1][2][3][4][5][6][7][8][9][10][11][12] and literature. Because of Banach [4], the Banachcontraction theorem (1922) is indeed the most significant consequence in the theory of fixed points in metric spaces.…”