On Fixed-Point Equations Involving Geraghty-Type Contractions with Solution to Integral Equation

Moirangthem Pradeep Singh; Yumnam Rohen; Naeem Saleem; Khairul Habib Alam; Kumam Anthony Singh; Asima Razzaque

doi:10.3390/math11244882

On Fixed-Point Equations Involving Geraghty-Type Contractions with Solution to Integral Equation

Moirangthem Pradeep Singh, Yumnam Rohen, Naeem Saleem^*, Khairul Habib Alam, Kumam Anthony Singh, Asima Razzaque

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

In this study, the authors verify fixed-point results for Geraghty contractions with a restricted co-domain of the auxiliary function in the context of generalized metric structure, namely the (Formula presented.) -metric space. This new idea of defining Geraghty contraction for self-operators generalizes a large number of previously published, closely related works on the presence and uniqueness of a fixed point in (Formula presented.) -metric space. Also, the outcomes are achieved by removing the continuity constraint of self-operators. We also provide examples to elaborate on the obtained results and an application to the integral equation to illustrate the significance in the literature.

Original language	English
Article number	4882
Journal	Mathematics
Volume	11
Issue number	24
DOIs	https://doi.org/10.3390/math11244882
Publication status	Published - Dec 2023
Externally published	Yes

Keywords

Geraghty-type contraction
S-metric space
fixed point

Access to Document

10.3390/math11244882

Cite this

@article{41560c3e620c41b989ed1029f95e5483,

title = "On Fixed-Point Equations Involving Geraghty-Type Contractions with Solution to Integral Equation",

abstract = "In this study, the authors verify fixed-point results for Geraghty contractions with a restricted co-domain of the auxiliary function in the context of generalized metric structure, namely the (Formula presented.) -metric space. This new idea of defining Geraghty contraction for self-operators generalizes a large number of previously published, closely related works on the presence and uniqueness of a fixed point in (Formula presented.) -metric space. Also, the outcomes are achieved by removing the continuity constraint of self-operators. We also provide examples to elaborate on the obtained results and an application to the integral equation to illustrate the significance in the literature.",

keywords = "Geraghty-type contraction, S-metric space, fixed point",

author = "Singh, {Moirangthem Pradeep} and Yumnam Rohen and Naeem Saleem and Alam, {Khairul Habib} and Singh, {Kumam Anthony} and Asima Razzaque",

note = "Publisher Copyright: {\textcopyright} 2023 by the authors.",

year = "2023",

month = dec,

doi = "10.3390/math11244882",

language = "English",

volume = "11",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "24",

}

TY - JOUR

T1 - On Fixed-Point Equations Involving Geraghty-Type Contractions with Solution to Integral Equation

AU - Singh, Moirangthem Pradeep

AU - Rohen, Yumnam

AU - Saleem, Naeem

AU - Alam, Khairul Habib

AU - Singh, Kumam Anthony

AU - Razzaque, Asima

PY - 2023/12

Y1 - 2023/12

N2 - In this study, the authors verify fixed-point results for Geraghty contractions with a restricted co-domain of the auxiliary function in the context of generalized metric structure, namely the (Formula presented.) -metric space. This new idea of defining Geraghty contraction for self-operators generalizes a large number of previously published, closely related works on the presence and uniqueness of a fixed point in (Formula presented.) -metric space. Also, the outcomes are achieved by removing the continuity constraint of self-operators. We also provide examples to elaborate on the obtained results and an application to the integral equation to illustrate the significance in the literature.

AB - In this study, the authors verify fixed-point results for Geraghty contractions with a restricted co-domain of the auxiliary function in the context of generalized metric structure, namely the (Formula presented.) -metric space. This new idea of defining Geraghty contraction for self-operators generalizes a large number of previously published, closely related works on the presence and uniqueness of a fixed point in (Formula presented.) -metric space. Also, the outcomes are achieved by removing the continuity constraint of self-operators. We also provide examples to elaborate on the obtained results and an application to the integral equation to illustrate the significance in the literature.

KW - Geraghty-type contraction

KW - S-metric space

KW - fixed point

UR - http://www.scopus.com/inward/record.url?scp=85180480167&partnerID=8YFLogxK

U2 - 10.3390/math11244882

DO - 10.3390/math11244882

M3 - Article

AN - SCOPUS:85180480167

SN - 2227-7390

VL - 11

JO - Mathematics

JF - Mathematics

IS - 24

M1 - 4882

ER -

On Fixed-Point Equations Involving Geraghty-Type Contractions with Solution to Integral Equation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this