On Polynomial <i>φ</i>-Contractions with Applications to Fractional Logistic Growth Equations
In this article, we introduce and study a novel class of polynomial <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-contractions, which simu...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-06-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/6/366 |
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| Summary: | In this article, we introduce and study a novel class of polynomial <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-contractions, which simultaneously generalizes classical polynomial contractions and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-contractions within a unified framework. We establish generalized fixed point theorems that encompass some results in the existing literature. Furthermore, we derive explicit error estimates and convergence rates for the associated Picard iteration, providing practical insights into the speed of convergence. Several illustrative examples, including higher-degree polynomial contractions, demonstrate the scope and applicability of our results. As an application, we prove existence and uniqueness results for solutions of a class of fractional logistic growth equations, highlighting the relevance of our theoretical contributions to nonlinear analysis and applied mathematics. |
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| ISSN: | 2504-3110 |