On stationary and nonstationary iterative methods for nonexpansive type mappings in Banach spaces

Rahul Shukla; Rajendra Pant; Adrian Petruşel

doi:10.1007/s13398-023-01435-5

On stationary and nonstationary iterative methods for nonexpansive type mappings in Banach spaces

Rahul Shukla, Rajendra Pant, Adrian Petruşel

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

Abstract

In this paper, we study stationary and nonstationary methods to approximate fixed points of a general class of nonexpansive type mappings in Banach spaces under certain conditions. We obtain weak convergence of a sequence of iterates of nonexpansive type mappings. We also present a stability result for nonstationary methods. We obtain data dependency analysis of the nonstationary methods. Moreover, we present a numerical example to demonstrate the convergence behaviour of the nonstationary methods. Finally, we pose an open problem.

Original language	English
Article number	100
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	117
Issue number	3
DOIs	https://doi.org/10.1007/s13398-023-01435-5
Publication status	Published - Jul 2023
Externally published	Yes

Keywords

Banach space
Nonexpnasive mapping
Nonstationary method

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s13398-023-01435-5

Cite this

@article{3807982fcbb14a7c9336e08b4d143693,

title = "On stationary and nonstationary iterative methods for nonexpansive type mappings in Banach spaces",

abstract = "In this paper, we study stationary and nonstationary methods to approximate fixed points of a general class of nonexpansive type mappings in Banach spaces under certain conditions. We obtain weak convergence of a sequence of iterates of nonexpansive type mappings. We also present a stability result for nonstationary methods. We obtain data dependency analysis of the nonstationary methods. Moreover, we present a numerical example to demonstrate the convergence behaviour of the nonstationary methods. Finally, we pose an open problem.",

keywords = "Banach space, Nonexpnasive mapping, Nonstationary method",

author = "Rahul Shukla and Rajendra Pant and Adrian Petru{\c s}el",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid.",

year = "2023",

month = jul,

doi = "10.1007/s13398-023-01435-5",

language = "English",

volume = "117",

journal = "Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas",

issn = "1578-7303",

publisher = "Springer-Verlag Italia s.r.l.",

number = "3",

}

TY - JOUR

T1 - On stationary and nonstationary iterative methods for nonexpansive type mappings in Banach spaces

AU - Shukla, Rahul

AU - Pant, Rajendra

AU - Petruşel, Adrian

PY - 2023/7

Y1 - 2023/7

N2 - In this paper, we study stationary and nonstationary methods to approximate fixed points of a general class of nonexpansive type mappings in Banach spaces under certain conditions. We obtain weak convergence of a sequence of iterates of nonexpansive type mappings. We also present a stability result for nonstationary methods. We obtain data dependency analysis of the nonstationary methods. Moreover, we present a numerical example to demonstrate the convergence behaviour of the nonstationary methods. Finally, we pose an open problem.

AB - In this paper, we study stationary and nonstationary methods to approximate fixed points of a general class of nonexpansive type mappings in Banach spaces under certain conditions. We obtain weak convergence of a sequence of iterates of nonexpansive type mappings. We also present a stability result for nonstationary methods. We obtain data dependency analysis of the nonstationary methods. Moreover, we present a numerical example to demonstrate the convergence behaviour of the nonstationary methods. Finally, we pose an open problem.

KW - Banach space

KW - Nonexpnasive mapping

KW - Nonstationary method

UR - https://www.scopus.com/pages/publications/85152520166

U2 - 10.1007/s13398-023-01435-5

DO - 10.1007/s13398-023-01435-5

M3 - Article

AN - SCOPUS:85152520166

SN - 1578-7303

VL - 117

JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

IS - 3

M1 - 100

ER -

On stationary and nonstationary iterative methods for nonexpansive type mappings in Banach spaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this