Stability of the <i>F</i><sup>∗</sup> Algorithm on Strong Pseudocontractive Mapping and Its Application

Stability of the <i>F</i><sup>∗</sup> Algorithm on Strong Pseudocontractive Mapping and Its Application

This paper investigates the stability of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>F</mi><mo>∗</mo></msup></semantics></math></inline-formula>...

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Bibliographic Details
Main Authors:	Taiwo P. Fajusigbe, Francis Monday Nkwuda, Hussaini Joshua, Kayode Oshinubi, Felix D. Ajibade, Jamiu Aliyu
Format:	Article
Language:	English
Published:	MDPI AG 2024-12-01
Series:	Mathematics
Subjects:	<i>F</i><sup>∗</sup> algorithm stability strong pseudocontractive mapping
Online Access:	https://www.mdpi.com/2227-7390/12/23/3811
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Summary:	This paper investigates the stability of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>F</mi><mo>∗</mo></msup></semantics></math></inline-formula> iterative algorithm applied to strongly pseudocontractive mappings within the context of uniformly convex Banach spaces. The study leverages both analytic and numerical methods to demonstrate the convergence and stability of the algorithm. In comparison to previous works, where weak-contraction mappings were utilized, the strongly pseudocontractive mappings used in this study preserve the convergence property, exhibit greater stability, and have broader applicability in optimization and fixed point theory. Additionally, this work shows that the type of mapping employed converges faster than those in earlier studies. The results are applied to a mixed-type Volterra–Fredholm nonlinear integral equation, and numerical examples are provided to validate the theoretical findings. Key contributions of this work include the following: (i) the use of strongly pseudocontractive mappings, which offer a more stable and efficient convergence rate compared to weak-contraction mappings; (ii) the application of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>F</mi><mo>∗</mo></msup></semantics></math></inline-formula> algorithm to a wider range of problems; and (iii) the proposal of future directions for improving convergence rates and exploring the algorithm’s behavior in Hilbert and reflexive Banach spaces.
ISSN:	2227-7390