Generalized α-nonexpansive mappings in Banach spaces

Rahul Shukla, Rajendra Pant, Manuel De la Sen

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

We consider a new type of monotone nonexpansive mappings in an ordered Banach space X with partial order ⪯. This new class of nonlinear mappings properly contains nonexpansive, firmly-nonexpansive and Suzuki-type generalized nonexpansive mappings and partially extends α-nonexpansive mappings. We obtain some existence theorems and weak and strong convergence theorems for the Mann iteration. Some useful examples are presented to illustrate the facts.

Original languageEnglish
Article number4
JournalFixed Point Theory and Algorithms for Sciences and Engineering
Volume2017
Issue number1
DOIs
Publication statusPublished - 1 Dec 2016
Externally publishedYes

Keywords

  • Opial property
  • condition (C)
  • generalized α-nonexpansive mapping
  • nonexpansive mapping
  • α-nonexpansive mapping

ASJC Scopus subject areas

  • Geometry and Topology
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Generalized α-nonexpansive mappings in Banach spaces'. Together they form a unique fingerprint.

Cite this