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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2024-12-01
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| Series: | Mathematics |
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| author | Taiwo P. Fajusigbe Francis Monday Nkwuda Hussaini Joshua Kayode Oshinubi Felix D. Ajibade Jamiu Aliyu |
| author_facet | Taiwo P. Fajusigbe Francis Monday Nkwuda Hussaini Joshua Kayode Oshinubi Felix D. Ajibade Jamiu Aliyu |
| author_sort | Taiwo P. Fajusigbe |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1e1b0c64c18f4a3cbefc676beb223396 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-1e1b0c64c18f4a3cbefc676beb2233962024-12-13T16:27:50ZengMDPI AGMathematics2227-73902024-12-011223381110.3390/math12233811Stability of the <i>F</i><sup>∗</sup> Algorithm on Strong Pseudocontractive Mapping and Its ApplicationTaiwo P. Fajusigbe0Francis Monday Nkwuda1Hussaini Joshua2Kayode Oshinubi3Felix D. Ajibade4Jamiu Aliyu5Department of Mathematics, Federal University Oye-Ekiti, Oye-Ekiti 371104, NigeriaDepartment of Mathematics, Federal University of Agriculture, Abeokuta 111101, NigeriaDepartment of Mathematics, Faculty of Science, University of Kerala, Kariavattom 695581, IndiaSchool of Informatics, Computing and Cyber System, Northern Arizona University, Flagstaf, AZ 86011, USADepartment of Mathematics, Federal University Oye-Ekiti, Oye-Ekiti 371104, NigeriaMathematics Division, Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7602, South AfricaThis 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.https://www.mdpi.com/2227-7390/12/23/3811<i>F</i><sup>∗</sup> algorithmstabilitystrong pseudocontractive mapping |
| spellingShingle | Taiwo P. Fajusigbe Francis Monday Nkwuda Hussaini Joshua Kayode Oshinubi Felix D. Ajibade Jamiu Aliyu Stability of the <i>F</i><sup>∗</sup> Algorithm on Strong Pseudocontractive Mapping and Its Application Mathematics <i>F</i><sup>∗</sup> algorithm stability strong pseudocontractive mapping |
| title | Stability of the <i>F</i><sup>∗</sup> Algorithm on Strong Pseudocontractive Mapping and Its Application |
| title_full | Stability of the <i>F</i><sup>∗</sup> Algorithm on Strong Pseudocontractive Mapping and Its Application |
| title_fullStr | Stability of the <i>F</i><sup>∗</sup> Algorithm on Strong Pseudocontractive Mapping and Its Application |
| title_full_unstemmed | Stability of the <i>F</i><sup>∗</sup> Algorithm on Strong Pseudocontractive Mapping and Its Application |
| title_short | Stability of the <i>F</i><sup>∗</sup> Algorithm on Strong Pseudocontractive Mapping and Its Application |
| title_sort | stability of the i f i sup ∗ sup algorithm on strong pseudocontractive mapping and its application |
| topic | <i>F</i><sup>∗</sup> algorithm stability strong pseudocontractive mapping |
| url | https://www.mdpi.com/2227-7390/12/23/3811 |
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