Some Results on Fixed Points and Approximation for a New Class of Mappings in CAT(0) Spaces

TL;DR

This paper generalizes fixed point concepts for a new class of mappings in CAT(0) spaces, establishing properties, inequalities, and fixed point theorems for $eta$-nonexpansive mappings.

Contribution

It introduces $eta$-nonexpansive mappings and extends fixed point theory in CAT(0) spaces with new properties and approximation results.

Findings

Established properties and inequalities for generalized mappings in CAT(0) spaces.

Proved fixed point and approximate fixed point theorems for $eta$-nonexpansive mappings.

Extended fixed point theory to a broader class of mappings in non-Euclidean spaces.

Abstract

We shall generalize the concept of $z=(1-t)x\oplus ty$ to $n$ times which contains to verifying some their properties and inequalities in CAT(0) spaces. In the sequel with introducing of $\alpha$-nonexpansive mappings, we obtain some fixed points and approximate fixed points theorems.