Common fixed points for $$(\psi -\varphi )$$-weak contractions type in b-metric spaces

Abstract

The aim of this paper is to prove the existence and uniqueness of common fixed points for a pair of $$(\psi -\varphi )$$ ( ψ - φ ) -weak contractive self-maps in the setting of b-metric spaces satisfying the minimal requirement of weakly compatibility, and other weak commuting properties as compatibility, R-weakly commuting and R-weakly commuting of types ($$A_T$$ A T ), ($$A_S$$ A S ) and ($$A_P$$ A P ). Also, we will analyze the convergence and stability of the Jungck-Noor iterative scheme for this class of pairs of mappings on b-metric spaces endowed with a convex structure.

Some New Types of α_(β^(-1) )-admissible Mappings and Fixed Point Results

“…Almost researchers in this direction have used 𝛼-admissible condition. For example see [8], [9], [10], [11], [12], [13], [14], [15].…”