BBC Russian

271 KiB

Open AccessProceeding Paper

Banach Fixed Point Theorem in Extended b_v(s)-Metric Spaces

by Anil Kumar

Comput. Sci. Math. Forum 2023, 7(1), 58; https://doi.org/10.3390/IOCMA2023-14736 - 30 May 2023

Viewed by 780

We define the class of extended

b_{v} (s)

-metric spaces by replacing the real number

s \geq 1

with a strictly increasing continuous function

ϕ

in the definition of a

b_{v} (s)

-metric space. Also, we presented [...] Read more.

We define the class of extended

b_{v} (s)

-metric spaces by replacing the real number

s \geq 1

with a strictly increasing continuous function

ϕ

in the definition of a

b_{v} (s)

-metric space. Also, we presented an example for this newly introduced space and exhibited that in a particular situation, the class of extended

b_{v} (s)

-metric spaces reduces to the class of

b_{v} (s)

-metric spaces. Afterwards, we establish a fixed point theorem which ensured the existence of a fixed point for the self-map satisfying the Banach contractive condition in the context of this newly defined space. Moreover, we compared the proved result with the existing fixed point theorems in the literature. Full article

(This article belongs to the Proceedings of The 1st International Online Conference on Mathematics and Applications)

13 pages, 308 KiB

Open AccessArticle

On Some Coupled Fixed Points of Generalized T-Contraction Mappings in a b_v(s)-Metric Space and Its Application

by Reny George, Zoran D. Mitrović and Stojan Radenović

Axioms 2020, 9(4), 129; https://doi.org/10.3390/axioms9040129 - 9 Nov 2020

Cited by 3 | Viewed by 2129

Abstract

Common coupled fixed point theorems for generalized T-contractions are proved for a pair of mappings

S : X \times X \to X

and

g : X \to X

in a

b_{v} (s)

-metric space, which generalize, extend, and improve some [...] Read more.

Common coupled fixed point theorems for generalized T-contractions are proved for a pair of mappings

S : X \times X \to X

and

g : X \to X

in a

b_{v} (s)

-metric space, which generalize, extend, and improve some recent results on coupled fixed points. As an application, we prove an existence and uniqueness theorem for the solution of a system of nonlinear integral equations under some weaker conditions and given a convergence criteria for the unique solution, which has been properly verified by using suitable example. Full article

(This article belongs to the Special Issue Theory and Application of Fixed Point)

Search Results (2)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Saved Queries

Search Filter Reset All

Years

Feature Papers

Subjects

Journals

Article Types

Countries / Regions

Search Results (2)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI