Stability of the F ∗ Algorithm on Strong Pseudocontractive Mapping and Its Application

Taiwo P. Fajusigbe, Francis Monday Nkwuda, Hussaini Joshua, Kayode Oshinubi (), Felix D. Ajibade and Jamiu Aliyu
Additional contact information
Taiwo P. Fajusigbe: Department of Mathematics, Federal University Oye-Ekiti, Oye-Ekiti 371104, Nigeria
Francis Monday Nkwuda: Department of Mathematics, Federal University of Agriculture, Abeokuta 111101, Nigeria
Hussaini Joshua: Department of Mathematics, Faculty of Science, University of Kerala, Kariavattom 695581, India
Kayode Oshinubi: School of Informatics, Computing and Cyber System, Northern Arizona University, Flagstaf, AZ 86011, USA
Felix D. Ajibade: Department of Mathematics, Federal University Oye-Ekiti, Oye-Ekiti 371104, Nigeria
Jamiu Aliyu: Mathematics Division, Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7602, South Africa

Mathematics, 2024, vol. 12, issue 23, 1-15

Abstract: This paper investigates the stability of the F ∗ 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 F ∗ 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.

Keywords: F ? algorithm; stability; strong pseudocontractive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/23/3811/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/23/3811/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:23:p:3811-:d:1534906

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().