Iterative approximation of common attractive points of further generalized hybrid mappings

TL;DR

This paper introduces new concepts of further generalized hybrid mappings and common attractive points, and develops an iterative process to approximate these points in Hilbert spaces, extending previous results.

Contribution

It defines new classes of mappings and attractive points, and generalizes iterative approximation methods for two mappings without requiring closedness.

Findings

Generalizes existing results on hybrid mappings

Introduces iterative process for two mappings in Hilbert spaces

Achieves approximation of common attractive points without closedness

Abstract

Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings (ii) to introduce the concept of common attractive points (CAP) (iii) to write and use Picard-Mann iterative process for two mappings. We approximate common attractive points of further generalized hybrid mappings by using iterative process due to Khan <cite>SHK</cite> generalized to the case of two mappings in Hilbert spaces without closedness assumption. Our results are generalizations and improvements of several results in the literature in different ways.