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

Source abstract

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.