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

13 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

Access to Document

10.1186/s13663-017-0597-9

Cite this

@article{13ed44a6ef2d45f2b8732221f0f088b4,

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.",

keywords = "Opial property, condition (C), generalized α-nonexpansive mapping, nonexpansive mapping, α-nonexpansive mapping",

author = "Rahul Shukla and Rajendra Pant and {De la Sen}, Manuel",

note = "Publisher Copyright: {\textcopyright} 2017, The Author(s).",

year = "2016",

month = dec,

day = "1",

doi = "10.1186/s13663-017-0597-9",

language = "English",

volume = "2017",

journal = "Fixed Point Theory and Algorithms for Sciences and Engineering",

issn = "1687-1820",

publisher = "SpringerOpen",

number = "1",

}

TY - JOUR

T1 - Generalized α-nonexpansive mappings in Banach spaces

AU - Shukla, Rahul

AU - Pant, Rajendra

AU - De la Sen, Manuel

PY - 2016/12/1

Y1 - 2016/12/1

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 - http://www.scopus.com/inward/record.url?scp=85013632674&partnerID=8YFLogxK

U2 - 10.1186/s13663-017-0597-9

DO - 10.1186/s13663-017-0597-9

M3 - Article

AN - SCOPUS:85013632674

SN - 1687-1820

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

Access to Document

Other files and links

Fingerprint

Cite this