An Efficient Iterative Scheme for Approximating the Fixed Point of a Function Endowed with Condition (<i>B<sub>γ,μ</sub></i>) Applied for Solving Infectious Disease Models

An Efficient Iterative Scheme for Approximating the Fixed Point of a Function Endowed with Condition (<i>B<sub>γ,μ</sub></i>) Applied for Solving Infectious Disease Models

The purpose of this paper is to construct a new fixed-point iterative scheme, called the Picard-like iterative scheme, for approximating the fixed point of a mapping that satisfies condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"...

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Bibliographic Details
Main Authors: Godwin Amechi Okeke, Akanimo Victor Udo, Rubayyi T. Alqahtani
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Mathematics
Subjects:
Picard-like iterative scheme
condition (<i>B<sub>γ</sub>,<sub>μ</sub></i>)
condition (I)
fixed point
boundary value problem
Green’s function
Online Access:https://www.mdpi.com/2227-7390/13/4/562
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Summary:The purpose of this paper is to construct a new fixed-point iterative scheme, called the Picard-like iterative scheme, for approximating the fixed point of a mapping that satisfies condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>B</mi><mrow><mi>γ</mi><mo>,</mo><mi>μ</mi></mrow></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> in the setting of a uniformly convex Banach space. We prove that this novel iterative scheme converges faster than some existing iterative schemes in the literature. Moreover, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-stability and almost <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-stability results are proven. Furthermore, we apply our results for approximating the solution of an integral equation that models the spread of some infectious diseases. Similarly, we also applied the results for approximating the solution of the boundary value problem by embedding Green’s function in our novel method. Our results extend and generalize other existing results in the literature.
ISSN:2227-7390

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