Cyclic G‐Ω-Weak Contraction-Weak Nonexpansive Mappings and Some Fixed Point Theorems in Metric Spaces

Abstract

This paper introduces novel concepts of joint $\left(Y,Z\right)$ cyclic $G‐{\Omega }_{S,T,\left(abef\right)}$-weak contraction and joint $\left(Y,Z\right)$ cyclic $G‐{\Omega }_{S,T,\left(abef\right)}$-weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic $G‐{\Omega }_{S,\left(abef\right)}$-weak contraction and cyclic $G‐{\Omega }_{S,\left(abef\right)}$-weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic ${\Omega }_{S,\left(abef\right)}$-weak contraction and cyclic ${\Omega }_{S,\left(abef\right)}$-weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references.