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

Nicola Fabiano; Zouaoui Bekri

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

Functional Analysis 2026-06-16 v1

Authors: Nicola Fabiano , Zouaoui Bekri

Abstract

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.

Keywords

fixed point Singh contractions boundary value problems Banach contraction principle generalized contractions

Cite

@article{arxiv.2607.01261,
  title  = {A Restatement of Fixed Point Existence: From Banach to Singh Contractions},
  author = {Nicola Fabiano and Zouaoui Bekri},
  journal= {arXiv preprint arXiv:2607.01261},
  year   = {2026}
}

Comments

10 pages