Generalized α-nonexpansive mappings in Banach spaces

Rahul Shukla; Rajendra Pant; Manuel De la Sen

doi:10.1186/s13663-017-0597-9

Generalized α-nonexpansive mappings in Banach spaces

Rahul Shukla
, Rajendra Pant
, Manuel De la Sen

Research output: Contribution to journal › Article › peer-review

15 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 language	English
Article number	4
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2017
Issue number	1
DOIs	https://doi.org/10.1186/s13663-017-0597-9
Publication status	Published - 1 Dec 2016
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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10.1186/s13663-017-0597-9

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title = "Generalized α-nonexpansive mappings in Banach spaces",

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.",

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AU - Pant, Rajendra

AU - De la Sen, Manuel

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N2 - 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.

AB - 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.

KW - Opial property

KW - condition (C)

KW - generalized α-nonexpansive mapping

KW - nonexpansive mapping

KW - α-nonexpansive mapping

UR - https://www.scopus.com/pages/publications/85013632674

U2 - 10.1186/s13663-017-0597-9

DO - 10.1186/s13663-017-0597-9

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AN - SCOPUS:85013632674

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VL - 2017

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

IS - 1

M1 - 4

ER -

Generalized α-nonexpansive mappings in Banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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