Fixed point theorems for (α,β)−(ψ,φ) -contractive mapping in b--metric spaces with some numerical results and applications

Abstract

In this paper, we introduce the concept of (α, β)-(ψ, ϕ)-contractive mapping in b-metric spaces. We establish some fixed point theorems for such mappings and also give an example supporting our results. Finally, we apply our main results to prove a fixed point theorem involving a cyclic mapping.

Common Fixed Point Theorem via Cyclic (α,β)–(ψ,φ)S-Contraction with Applications

“…Remark 2. In Theorem 3.2 of [7], the continuity of mapping is necessary; however, we relaxed this condition in Corollary 2.…”

“…Motivated by the work in [7,19], we present the notion of cyclic (α, β) − (ψ, ϕ) s -rational-type contraction in b-metric space, and using this notion we study common fixed point theorems, which generalize many recent results. As an application of our work, we study the existence of a unique bounded common solution to the system of functional equations that arise in dynamic programming, mathematical optimization, and in computer programming.…”

“…They proved the Banach contraction principle in b-metric spaces. Afterwards, several papers were published by many authors dealing with the existence of a fixed point in b-metric spaces (see [4][5][6][7][8][9][10][11][12][13][14][15][16][17]).…”

“…Isik et al [19] proved fixed point theorems under the T-cyclic-(α, β)-contractive condition in metric space. Recently, Yamaod and Sintunavarat [7] proposed the notion of (α, β) − (ψ, ϕ)-contraction in b-metric spaces and proved fixed point theorems for this class of contraction.…”

Fuzzy b-Metric Spaces: Fixed Point Results for ψ-Contraction Correspondences and Their Application

“…This modification is the generalization of the "probabilistic metric space" to the fuzzy situation. Afterwards the "fuzzy b-metric space" was defined in [7] which generalizes the "fuzzy metric space" and "b-metric space".…”