Convergence and <i>ω</i><sup>2</sup>-Stability Analysis of a Hybrid-Type Iterative Scheme with Application to Functional Delay Differential Equations
The purpose of this article is to analyze a hybrid-type iterative algorithm for a class of generalized non-expansive mappings satisfying the Garcia-Falset property in uniformly convex Banach spaces. Some existing results for such mappings have been obtained using the given algorithm. The <inline-...
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2025-06-01
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| author | Safeer Hussain Khan Hina Dilawer Hira Iqbal Mujahid Abbas |
| author_facet | Safeer Hussain Khan Hina Dilawer Hira Iqbal Mujahid Abbas |
| author_sort | Safeer Hussain Khan |
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| description | The purpose of this article is to analyze a hybrid-type iterative algorithm for a class of generalized non-expansive mappings satisfying the Garcia-Falset property in uniformly convex Banach spaces. Some existing results for such mappings have been obtained using the given algorithm. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>ω</mi><mn>2</mn></msup></semantics></math></inline-formula>-stability of the iterative process is also studied. Using some examples, numerical experiments are conducted by comparing this iterative algorithm with different well-known iterative schemes. It is concluded that this iterative algorithm converges faster to the fixed point and is preferable over the previously known iterative schemes using the Garcia-Falset property. A weak solution of the Volterra–Stieltjes-type delay functional differential equation is presented to demonstrate the significance of the proposed results. |
| format | Article |
| id | doaj-art-64366758d0de40c582787bbd851bc8c8 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-64366758d0de40c582787bbd851bc8c82025-08-20T03:26:57ZengMDPI AGAxioms2075-16802025-06-0114647510.3390/axioms14060475Convergence and <i>ω</i><sup>2</sup>-Stability Analysis of a Hybrid-Type Iterative Scheme with Application to Functional Delay Differential EquationsSafeer Hussain Khan0Hina Dilawer1Hira Iqbal2Mujahid Abbas3Department of Mathematics and Statistics, North Carolina A&T State University, Greensboro, NC 27411, USADepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Lahore 54000, PakistanDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Lahore 54000, PakistanDepartment of Mechanical Engineering Sciences, University of Johannesburg, Johannesburg 2006, South AfricaThe purpose of this article is to analyze a hybrid-type iterative algorithm for a class of generalized non-expansive mappings satisfying the Garcia-Falset property in uniformly convex Banach spaces. Some existing results for such mappings have been obtained using the given algorithm. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>ω</mi><mn>2</mn></msup></semantics></math></inline-formula>-stability of the iterative process is also studied. Using some examples, numerical experiments are conducted by comparing this iterative algorithm with different well-known iterative schemes. It is concluded that this iterative algorithm converges faster to the fixed point and is preferable over the previously known iterative schemes using the Garcia-Falset property. A weak solution of the Volterra–Stieltjes-type delay functional differential equation is presented to demonstrate the significance of the proposed results.https://www.mdpi.com/2075-1680/14/6/475convergenceGarcia-Falset mappingstabilityiterative algorithm |
| spellingShingle | Safeer Hussain Khan Hina Dilawer Hira Iqbal Mujahid Abbas Convergence and <i>ω</i><sup>2</sup>-Stability Analysis of a Hybrid-Type Iterative Scheme with Application to Functional Delay Differential Equations Axioms convergence Garcia-Falset mapping stability iterative algorithm |
| title | Convergence and <i>ω</i><sup>2</sup>-Stability Analysis of a Hybrid-Type Iterative Scheme with Application to Functional Delay Differential Equations |
| title_full | Convergence and <i>ω</i><sup>2</sup>-Stability Analysis of a Hybrid-Type Iterative Scheme with Application to Functional Delay Differential Equations |
| title_fullStr | Convergence and <i>ω</i><sup>2</sup>-Stability Analysis of a Hybrid-Type Iterative Scheme with Application to Functional Delay Differential Equations |
| title_full_unstemmed | Convergence and <i>ω</i><sup>2</sup>-Stability Analysis of a Hybrid-Type Iterative Scheme with Application to Functional Delay Differential Equations |
| title_short | Convergence and <i>ω</i><sup>2</sup>-Stability Analysis of a Hybrid-Type Iterative Scheme with Application to Functional Delay Differential Equations |
| title_sort | convergence and i ω i sup 2 sup stability analysis of a hybrid type iterative scheme with application to functional delay differential equations |
| topic | convergence Garcia-Falset mapping stability iterative algorithm |
| url | https://www.mdpi.com/2075-1680/14/6/475 |
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