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

Abstract

In this paper, we introduce the notion of cyclic ( α , β ) - ( ψ , φ ) s -rational-type contraction in b-metric spaces, and using this contraction, we prove common fixed point theorems. Our work generalizes many existing results in the literature. In order to highlight the usefulness of our results, applications to functional equations are given.

On Some Common Fixed Point Results for Weakly Contraction Mappings with Application

“…In 2019, Hussain et al studied the existence and uniqueness of periodic common fixed point for pairs of mappings via rational type contraction in [7]. After that, in [8], the authors obtained fixed point theorems for cyclic ðα, βÞ − ðψ, ϕÞ s -rational type contractions and discussed the existence of a unique solution to nonlinear fractional differential equations. Also using rational type contractive conditions, Hussain et al [9] got the existence and uniqueness of a common n-tupled fixed point for a pair of mappings.…”

Common Fixed Point Results for Generalized g − α

“…In 2019, Hussain et al studied the existence and uniqueness of a periodic common fixed point for pairs of mappings via rational type contraction in [7]. After that, authors obtained fixed point theorems for L − cyclic ðα, βÞ s − contractions and cyclic ðα, βÞ − ðψ, ϕÞ s − rational type contractions and discussed the existence of a unique solution to nonlinear fractional differential equations in [8,9], respectively. Also using rational type contractive conditions, Hussain et al [10] got the existence and uniqueness of common n − tupled fixed point for a pair of mappings.…”