Fixed Point Results in Modular b-Metric-like Spaces with an Application

Fixed Point Results in Modular b-Metric-like Spaces with an Application

In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</...

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Bibliographic Details
Main Authors: Nizamettin Ufuk Bostan, Banu Pazar Varol
Format: Article
Language:English
Published: MDPI AG 2024-10-01
Series:Axioms
Subjects:
modular b-metric-like space
fixed point
contraction principle
integral equation
Online Access:https://www.mdpi.com/2075-1680/13/10/726
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Summary:In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula>-convergence, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula>-Cauchy sequence, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula>-completeness and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula>-contraction. The existence and uniqueness of fixed points in the modular b-metric-like space are handled. Moreover, we give some examples and an application to an integral equation to illustrate the usability of the obtained results.
ISSN:2075-1680

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