Some Valid Generalizations of Boyd and Wong Inequality andψ,ϕ-Weak Contraction in Partially Orderedb−Metric Spaces

Abstract

In this manuscript, we use ψ,ϕ-weak contraction to generalize coincidence point results which are established in the context of partially ordered b-metric spaces. The presented work explicitly generalized some recent results from the existing literature. Examples are also provided to show the authenticity of the established work.

Common Fixed Point Theorems for Weakly Contractions in Rectangular b -Metric Spaces with Supportive Applications

“…For example, in [33], the authors obtained the fixed point results involving α-ψ contraction conditions and applied them to solve quadratic integral equations. In [34], Jamal et al used ðψ, ϕÞ-weak contraction to extend coincidence point theorems obtained in partially ordered b -metric spaces. Set…”

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

“…Since then, many authors (for example, [31][32][33][34][35][36][37][38][39][40][41][42]) obtained generalizations and extensions of the weak contraction principle. Recently, in [43], Jamal et al used ðψ, ϕÞ-weak contraction to generalize coincidence point results which are established in the context of partially ordered b-metric spaces.…”

Common Fixed Point Results for Generalized g − α

“…Recently, Samet et al [15] introduced the concept of α − admissible and α − ψ − contractive mappings and presented fixed point theorems for them. In [16], Jamal et al used ðψ, ϕÞ − weak contraction to generalize coincidence point results which are established in the context of partially ordered b − metric spaces. In [17,18], Zoto et al studied generalized α s p contractive mappings and ðα − ψ, ϕÞ − contractions in b − metric−like space.…”

“…In [17,18], Zoto et al studied generalized α s p contractive mappings and ðα − ψ, ϕÞ − contractions in b − metric−like space. Recently, in [16], Jamal et al used ðψ, ϕÞ − weak contraction to generalize coincidence point results which are established in the context of partially ordered b − metric spaces. Abu-Donia et al [19] proved the uniqueness and existence of the fixed points for five mappings from a complete intuitionistic fuzzy 3 − metric space into itself under weak compatible of type ðαÞ and asymptotically regular.…”