Some fixed point and stability results in b-metric-like spaces with an application to integral equations on time scales

Zeynep Kalkan; Aynur Şahin; Ahmad Aloqaily; Nabil Mlaiki

doi:10.3934/math.2024556

Some fixed point and stability results in b-metric-like spaces with an application to integral equations on time scales

Zeynep Kalkan, Aynur Şahin, Ahmad Aloqaily, Nabil Mlaiki

School of Computer, Data and Mathematical Sciences

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

2 Citations (Scopus)

4 Downloads (Pure)

Abstract

This paper presents the stability theorem for the T-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning T-mean nonexpansive mappings within b-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically.

Original language	English
Pages (from-to)	11335-11351
Number of pages	17
Journal	AIMS Mathematics
Volume	9
Issue number	5
DOIs	https://doi.org/10.3934/math.2024556
Publication status	Published - 2024

Bibliographical note

Publisher Copyright:
© 2024 the Author(s), licensee AIMS Press.

Keywords

b-metric-like space
fixed point
Hammerstein integral equation
stability
T-mean nonexpansive mapping
time scale

Access to Document

10.3934/math.2024556Licence: CC BY

Full textFinal published version, 250 KBLicence: CC BY

Cite this

@article{9b7afc859a6a43cc80d40b86ad6161ff,

title = "Some fixed point and stability results in b-metric-like spaces with an application to integral equations on time scales",

abstract = "This paper presents the stability theorem for the T-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning T-mean nonexpansive mappings within b-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically.",

keywords = "b-metric-like space, fixed point, Hammerstein integral equation, stability, T-mean nonexpansive mapping, time scale",

author = "Zeynep Kalkan and Aynur {\c S}ahin and Ahmad Aloqaily and Nabil Mlaiki",

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

year = "2024",

doi = "10.3934/math.2024556",

language = "English",

volume = "9",

pages = "11335--11351",

journal = "AIMS Mathematics",

issn = "2473-6988",

publisher = "AIMS Press",

number = "5",

}

TY - JOUR

T1 - Some fixed point and stability results in b-metric-like spaces with an application to integral equations on time scales

AU - Kalkan, Zeynep

AU - Şahin, Aynur

AU - Aloqaily, Ahmad

AU - Mlaiki, Nabil

PY - 2024

Y1 - 2024

N2 - This paper presents the stability theorem for the T-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning T-mean nonexpansive mappings within b-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically.

AB - This paper presents the stability theorem for the T-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning T-mean nonexpansive mappings within b-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically.

KW - b-metric-like space

KW - fixed point

KW - Hammerstein integral equation

KW - stability

KW - T-mean nonexpansive mapping

KW - time scale

UR - http://www.scopus.com/inward/record.url?scp=85191449067&partnerID=8YFLogxK

U2 - 10.3934/math.2024556

DO - 10.3934/math.2024556

M3 - Article

AN - SCOPUS:85191449067

SN - 2473-6988

VL - 9

SP - 11335

EP - 11351

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 5

ER -

Some fixed point and stability results in b-metric-like spaces with an application to integral equations on time scales

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this