On Iteration Sn for Operators with Condition (D)

Abstract

A recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure Sn. Issues related to data dependence and the stability of this iterative process are also being studied. Our study is performed in the framework of Banach spaces, in which the symmetry of the associated metric is a fundamental axiom and plays a key role while proving many results of this paper.

Abstract Fixed-Point Theorems and Fixed-Point Iterative Schemes

“…Thus, the aim of this collection of papers is to cover some of the recent advancements in abstract research and in developing new useful applications. The specific topics mainly include both fixed-point theorems in generalized metric spaces and Banach spaces (see [1][2][3][4][5][6][7]) and fixed-point iterative schemes along with the convergence analysis of proposed solving algorithms (see [8][9][10][11][12][13][14]). In particular, we point the attention of the reader on the applications of fixed-point arguments to the context of various classes of differential equations (see [15][16][17][18]); for a similar approach to integral equations, see [19].…”