Fixed point approximation of contractive-like mappings using a stable iterative family and its dynamics via quadratic polynomials
This study aims at presenting a novel bi-parametric family of iterative methods for computing the fixed points of a contractive-like mapping. We thoroughly analyze the strong and stable convergence of the proposed technique and explore its applicability across various problem domains. Regarding con...
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| Format: | Article |
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Vilnius Gediminas Technical University
2025-07-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vilniustech.lt/index.php/MMA/article/view/21763 |
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| author | Munish Kansal Higinio Ramos Litika Rani |
| author_facet | Munish Kansal Higinio Ramos Litika Rani |
| author_sort | Munish Kansal |
| collection | DOAJ |
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This study aims at presenting a novel bi-parametric family of iterative methods for computing the fixed points of a contractive-like mapping. We thoroughly analyze the strong and stable convergence of the proposed technique and explore its applicability across various problem domains. Regarding convergence, it is proven that for several operators, the Mann iteration is analogous to the proposed multi-step class, and vice-versa. Moreover, numerical tests demonstrate the superior performance of the new procedures compared to existing three-step schemes. We further examine the dynamic behavior of several fixed-point iterative techniques when applied to quadratic polynomials. Based on the outcomes of these experiments, it can be concluded that the proposed family demonstrates both validity and effectiveness.
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| format | Article |
| id | doaj-art-d798c0954aa444bb8810632cc83fe5b3 |
| institution | Kabale University |
| issn | 1392-6292 1648-3510 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj-art-d798c0954aa444bb8810632cc83fe5b32025-08-20T03:29:39ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102025-07-0130310.3846/mma.2025.21763Fixed point approximation of contractive-like mappings using a stable iterative family and its dynamics via quadratic polynomialsMunish Kansal0Higinio Ramos1Litika Rani2https://orcid.org/0000-0002-3774-421XDepartment of Mathematics, Thapar Institute of Engineering and Technology, 147004 Patiala, IndiaScientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain; Escuela Politécnica Superior de Zamora, Universidad de Salamanca, Campus Viriato, 49022 Zamora, SpainDepartment of Mathematics, Thapar Institute of Engineering and Technology, 147004 Patiala, India This study aims at presenting a novel bi-parametric family of iterative methods for computing the fixed points of a contractive-like mapping. We thoroughly analyze the strong and stable convergence of the proposed technique and explore its applicability across various problem domains. Regarding convergence, it is proven that for several operators, the Mann iteration is analogous to the proposed multi-step class, and vice-versa. Moreover, numerical tests demonstrate the superior performance of the new procedures compared to existing three-step schemes. We further examine the dynamic behavior of several fixed-point iterative techniques when applied to quadratic polynomials. Based on the outcomes of these experiments, it can be concluded that the proposed family demonstrates both validity and effectiveness. https://journals.vilniustech.lt/index.php/MMA/article/view/21763fixed point iterationBanach spaceMann iterationΦ-stabilitycontractive-like operator |
| spellingShingle | Munish Kansal Higinio Ramos Litika Rani Fixed point approximation of contractive-like mappings using a stable iterative family and its dynamics via quadratic polynomials Mathematical Modelling and Analysis fixed point iteration Banach space Mann iteration Φ-stability contractive-like operator |
| title | Fixed point approximation of contractive-like mappings using a stable iterative family and its dynamics via quadratic polynomials |
| title_full | Fixed point approximation of contractive-like mappings using a stable iterative family and its dynamics via quadratic polynomials |
| title_fullStr | Fixed point approximation of contractive-like mappings using a stable iterative family and its dynamics via quadratic polynomials |
| title_full_unstemmed | Fixed point approximation of contractive-like mappings using a stable iterative family and its dynamics via quadratic polynomials |
| title_short | Fixed point approximation of contractive-like mappings using a stable iterative family and its dynamics via quadratic polynomials |
| title_sort | fixed point approximation of contractive like mappings using a stable iterative family and its dynamics via quadratic polynomials |
| topic | fixed point iteration Banach space Mann iteration Φ-stability contractive-like operator |
| url | https://journals.vilniustech.lt/index.php/MMA/article/view/21763 |
| work_keys_str_mv | AT munishkansal fixedpointapproximationofcontractivelikemappingsusingastableiterativefamilyanditsdynamicsviaquadraticpolynomials AT higinioramos fixedpointapproximationofcontractivelikemappingsusingastableiterativefamilyanditsdynamicsviaquadraticpolynomials AT litikarani fixedpointapproximationofcontractivelikemappingsusingastableiterativefamilyanditsdynamicsviaquadraticpolynomials |