Zouaoui Bekri | Searcharxiv

arXiv2026

A Restatement of Fixed Point Existence: From Banach to Singh Contractions

This paper presents a reformulation of classical existence and uniqueness results for second-order boundary value problems (BVPs). For Singh contractions, we allow $T^p$ to satisfy the condition, providing greater flexibility. Examples illustrate the applicability of all results. The work highlights the utility of generalized contractions in differential equations, particularly when the Banach contraction principle fails.

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arXiv2025

Fixed Point Theory For Singh-Chatterjea Type Contractive Mappings

In this paper, we introduce a new contraction condition that combines the framework of Singh's extension with the classical Chatterjea contraction. This generalized form, called the Singh-Chatterjea contraction, is defined on the p-th iterate of a mapping. We establish fixed point theorems for such mappings in complete metric spaces and show that our results extend and unify both Singh's and Chatterjea's classical fixed point theorems. Illustrative examples and a simple numerical implementation are provided to demonstrate the applicability of the obtained results.

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