Equivalence of certain iteration processes obtained by two new classes of operators

Mujahid Abbas; Rizwan Anjum; Vasile Berinde

doi:10.3390/math9182292

Equivalence of certain iteration processes obtained by two new classes of operators

Mujahid Abbas
, Rizwan Anjum
, Vasile Berinde

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

20 Citations (Scopus)

Abstract

The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.

Original language	English
Article number	2292
Journal	Mathematics
Volume	9
Issue number	18
DOIs	https://doi.org/10.3390/math9182292
Publication status	Published - Sept 2021
Externally published	Yes

Keywords

Fixed point
Ishikawa iteration
Krasnoselskij iteration
Mann iteration

ASJC Scopus subject areas

Computer Science (miscellaneous)
General Mathematics
Engineering (miscellaneous)

Access to Document

10.3390/math9182292

Cite this

@article{e6f1cb4914264bb4acd1f401b60341f1,

title = "Equivalence of certain iteration processes obtained by two new classes of operators",

abstract = "The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.",

keywords = "Fixed point, Ishikawa iteration, Krasnoselskij iteration, Mann iteration",

author = "Mujahid Abbas and Rizwan Anjum and Vasile Berinde",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = sep,

doi = "10.3390/math9182292",

language = "English",

volume = "9",

journal = "Mathematics",

issn = "2227-7390",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "18",

}

TY - JOUR

T1 - Equivalence of certain iteration processes obtained by two new classes of operators

AU - Abbas, Mujahid

AU - Anjum, Rizwan

AU - Berinde, Vasile

PY - 2021/9

Y1 - 2021/9

N2 - The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.

AB - The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.

KW - Fixed point

KW - Ishikawa iteration

KW - Krasnoselskij iteration

KW - Mann iteration

UR - https://www.scopus.com/pages/publications/85115336427

U2 - 10.3390/math9182292

DO - 10.3390/math9182292

M3 - Article

AN - SCOPUS:85115336427

SN - 2227-7390

VL - 9

JO - Mathematics

JF - Mathematics

IS - 18

M1 - 2292

ER -

Equivalence of certain iteration processes obtained by two new classes of operators

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this