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

Abstract

This paper introduces novel concepts of joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-weak contraction and joint ðY , ZÞ cyclic G‐ΩS,T ,ðabef Þ-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‐ΩS,ðabef Þ-weak contraction and cyclic G‐ΩS,ðabef Þ-weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic ΩS,ðabef Þ-weak contraction and cyclic ΩS,ðabef Þ-weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references.