Fixed point results in $ b $-metric spaces with applications to integral equations

Alamri, Badriah A. S.; Ahmad, Jamshaid

doi:10.3934/math.2023476

Cited by 3 publications

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 2017 (7) ,Muhammad Usman Ali introduced the idea of b-multiplicative metric spaces which provides the descriptions https://www.indjst.org/ of distances increased versatility and enables the detection of some kinds of non-linearities that metric spaces could lack. Recently few authors have established some applications for integral equations (8) ,differential equations (9) ,and coupled fixed point problems (10) .…”

Section: Introductionmentioning

confidence: 99%

Application of Fixed Point Theorems to Differential Equation in b-Multiplicative Metric Spaces

Jarvisvivin,

Dharsini

2024

IJST

View full text Add to dashboard Cite

Objectives: In this manuscript, some fixed point theorems have been provided in b-multiplicative metric spaces. Methods: We proved the unique fixed point theorems using the Banach contraction principle and generalized Lipschitz contractive mappings. Findings: We established the P Property and the T-Stability of Picard’s iteration in b-multiplicative metric spaces. We also provide an example to demonstrate the result. Novelty: Using our results, we obtained the existence and uniqueness of solutions for ordinary multiplicative differential equations with initial value problems. 2020 Mathematics Subject Classification: 47H10, 54H25. Keywords: Fixed Point, Generalized Lipschitz Contractive, Picard’s iteration, b-Multiplicative Metric Space (b − MMS), T -Stability, Differential equation

show abstract

Section: Introductionmentioning

confidence: 99%

Application of Fixed Point Theorems to Differential Equation in b-Multiplicative Metric Spaces

Jarvisvivin,

Dharsini

2024

IJST

View full text Add to dashboard Cite

show abstract

Some fixed point results concerning various contractions in extended b- metric space endowed with a graph

Kumar,

Mehra,

Santina

et al. 2025

Results in Applied Mathematics

View full text Add to dashboard Cite

Stability analysis through the Bielecki metric to nonlinear fractional integral equations of $ n $-product operators

Paul,

Mishra

2024

MATH

View full text Add to dashboard Cite

<abstract><p>This work is devoted to the analysis of Hyers, Ulam, and Rassias types of stabilities for nonlinear fractional integral equations with $ n $-product operators. In some special cases, our considered integral equation is related to an integral equation which arises in the study of the spread of an infectious disease that does not induce permanent immunity. $ n $-product operators are described here in the sense of Riemann-Liouville fractional integrals of order $ \sigma_i \in (0, 1] $ for $ i\in \{1, 2, \dots, n\} $. Sufficient conditions are provided to ensure Hyers-Ulam, $ \lambda $-semi-Hyers-Ulam, and Hyers-Ulam-Rassias stabilities in the space of continuous real-valued functions defined on the interval $ [0, a] $, where $ 0 < a < \infty $. Those conditions are established by applying the concept of fixed-point arguments within the framework of the Bielecki metric and its generalizations. Two examples are discussed to illustrate the established results.</p></abstract>

show abstract

Fixed point results in $ b $-metric spaces with applications to integral equations

Cited by 3 publications

References 25 publications

Application of Fixed Point Theorems to Differential Equation in b-Multiplicative Metric Spaces

Application of Fixed Point Theorems to Differential Equation in b-Multiplicative Metric Spaces

Some fixed point results concerning various contractions in extended b- metric space endowed with a graph

Stability analysis through the Bielecki metric to nonlinear fractional integral equations of $ n $-product operators

Contact Info

Product

Resources

About