Fixed Point of Almost Contraction in$b$-Metric Spaces

Abstract

In this paper, we introduce a generalized multivalued ( α , L)-almost contraction in the b -metric space. Furthermore, we prove the existence and uniqueness of the fixed point for a specific mapping. The result presented in this paper extends some of the earlier results in the existing literature. Moreover, some examples are given to illuminate the usability of the obtained results.

On the Admissibility of the Fixed Points Set of a Mapping with Respect to Another Mapping

“…Clearly, taking g ≡ 0 and F(s) = Ls in Corollary 1, we refind these results. For additional references related to (h, L)-weak contractions and their generalizations, see e.g., [17,19,[21][22][23][24][25] and the 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.…”

EXTENDED Gb-METRIC SPACES AND SOME FIXED POINT RESULTS WITH AN APPLICATION TO FREDHOLM INTEGRAL EQUATION V. GUPTA, O. EGE AND R. SAINI

“…Bakhtin [6] popularized the theory of b-metric spaces and Czerwik [8] extended the results of b-metric spaces. For some recent works on b-metric spaces, see [14,17,18]. Mustafa and Sims [22] familiarized an upgraded version of the generalized metric, that is, G-metric space.…”