Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process

Abstract

In this article, we prove some strong and weak convergence theorems for quasi-nonexpansive multivalued mappings in Banach spaces. The iterative process used is independent of Ishikawa iterative process and converges faster. Some examples are provided to validate our results. Our results extend and unify some results in the contemporary literature.

Approximation of the Fixed Point of Multivalued Quasi-Nonexpansive Mappings via a Faster Iterative Process with Applications

“…With a series of numerical experiments and an analytical proof, it is established that the Picard-Ishikawa hybrid iterative process, recently introduced by Okeke [3], has the same rate of convergence as the CR iterative process, introduced by Chugh et al [8]. Our results improve, extend, and generalize several known results in the literature [18][19][20].…”

Fixed point approximation of multivalued rho-quasi-nonexpansive mappings in modular function spaces

“…They approximated fixed points by convergence of a Mann iterative process (a one-step process) applied on multivalued ρ-nonexpansive mappings in modular function spaces. Khan et al [7] constructed a three-step iterative process for multivalued mappings in Banach spaces. This process is independent of both Mann and Ishikawa iterative processes in the sense that neither reduce to the other.…”

The iterative procedure with errors for approximating fixed points of multivalued quasi-nonexpansive mappings

“…Based on the above lemma, Song and Wang [22] modified the iteration scheme used in [11] and improved the results presented therein. This scheme reads as follows:…”

“…al. [11] introduced new three iterative procedures and proved some strong and weak convergence theorems for quasi nonexpansive multivalued mappings in Banach spaces. They showed that the iterative process used is independent of Ishikawa iterative process and converges faster.…”

“…al. [11], we use the iterative schemes with errors to approximate fixed points of a multivalued quasi-nonexpansive mappings in Banach spaces and prove strong and weak convergence theorems of the proposed iteration.…”