Approximation of fixed points for a new class of generalized non-expansivmappings in Banach spaces

Thabet Abdeljawad; Nazli Kadioglu Karaca; Isa Yildirim; Aiman Mukheimer

doi:10.3934/math.2024584

Approximation of fixed points for a new class of generalized non-expansivmappings in Banach spaces

Thabet Abdeljawad^*, Nazli Kadioglu Karaca, Isa Yildirim, Aiman Mukheimer

^*Corresponding author for this work

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

Abstract

In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition B_γ,µ. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.

Original language	English
Pages (from-to)	11958-11974
Number of pages	17
Journal	AIMS Mathematics
Volume	9
Issue number	5
DOIs	https://doi.org/10.3934/math.2024584
Publication status	Published - 2024
Externally published	Yes

Keywords

fixed point
generalized non-expansive mappings
uniformly convex Banach spacMathematics

Access to Document

10.3934/math.2024584

Cite this

@article{f5a611ebe90b45e6b33717281815ca12,

title = "Approximation of fixed points for a new class of generalized non-expansivmappings in Banach spaces",

abstract = "In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition Bγ,µ. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.",

keywords = "fixed point, generalized non-expansive mappings, uniformly convex Banach spacMathematics",

author = "Thabet Abdeljawad and Karaca, {Nazli Kadioglu} and Isa Yildirim and Aiman Mukheimer",

note = "Publisher Copyright: {\textcopyright} 2024 the Author(s), licensee AIMS Press.",

year = "2024",

doi = "10.3934/math.2024584",

language = "English",

volume = "9",

pages = "11958--11974",

journal = "AIMS Mathematics",

issn = "2473-6988",

publisher = "AIMS Press",

number = "5",

}

TY - JOUR

T1 - Approximation of fixed points for a new class of generalized non-expansivmappings in Banach spaces

AU - Abdeljawad, Thabet

AU - Karaca, Nazli Kadioglu

AU - Yildirim, Isa

AU - Mukheimer, Aiman

PY - 2024

Y1 - 2024

N2 - In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition Bγ,µ. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.

AB - In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition Bγ,µ. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.

KW - fixed point

KW - generalized non-expansive mappings

KW - uniformly convex Banach spacMathematics

UR - http://www.scopus.com/inward/record.url?scp=85188730968&partnerID=8YFLogxK

U2 - 10.3934/math.2024584

DO - 10.3934/math.2024584

M3 - Article

AN - SCOPUS:85188730968

SN - 2473-6988

VL - 9

SP - 11958

EP - 11974

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 5

ER -

Approximation of fixed points for a new class of generalized non-expansivmappings in Banach spaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this