On an efficient iterative scheme for a class of generalized nonexpansive operators in Banach spaces

Author:

Ahmad Fayyaz1,Ullah Kifayat1,Ahmad Junaid2ORCID,Bilal Hazrat3

Affiliation:

1. Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan

2. Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad-44000, Pakistan

3. Department of Mathematics, University of Science and Technology Bannu, Bannu 28100, Khyber Pakhtunkhwa, Pakistan

Abstract

The main purpose of this work is to connect the recently introduced iterative approximation scheme known as [Formula: see text]-iterative scheme with the class of generalized [Formula: see text]-nonexpansive mappings. We consider the setting of a Banach space to prove our weak and strong convergence results. Once again, we prove that the class of [Formula: see text]-nonexpansive mapping includes properly the classes of Suzuki nonexpansive, generalized [Formula: see text]-nonexpansive and as well Reich–Suzuki type nonexpansive mappings by providing a numerical example. Eventually, we prove that [Formula: see text]-iterative scheme of this example is essentially more efficient than the other well-known iterative scheme of the literature. The presented work is new and extends some other well-known results in the iterations theory.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

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