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

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.