Strong and Δ-Convergence Fixed-Point Theorems Using Noor Iterations

Abstract

A wide range of new research articles in artificial intelligence, logic programming, and other applied sciences are based on fixed-point theorems. The aim of this article is to present an approximation method for finding the fixed point of generalized Suzuki nonexpansive mappings on hyperbolic spaces. Strong and Δ-convergence theorems are proved using the Noor iterative process for generalized Suzuki nonexpansive mappings (GSNM) on uniform convex hyperbolic spaces. Due to the richness of uniform convex hyperbolic spaces, the results of this paper can be used as an extension and generalization of many famous results in Banach spaces together with CAT(0) spaces.

A Modified Iterative Approach for Fixed Point Problem in Hadamard Spaces

“…Its usefulness mostly hinges on the availability of solutions to mathematical problems generated from systems engineering [4] and computer science [5]. Because of its novel development as a confluence of analysis [6,7] and geometry [8], the theory of fixed points has also become a powerful and vital instrument for the study of nonlinear problems [9]. As such, a choice between several distinct iteration approaches must be made, taking important aspects into account.…”