Fixed point methodologies for $\psi_{\mathbb{A}}$-contraction mappings over $\mathbf{C}^{*}$-algebra with applications

Mohamed Gamal; Hasanen A. Hammad; Saleh  Omran

doi:10.5269/bspm.77457

Mohamed Gamal
Hasanen A. Hammad Sohag University
Saleh Omran

Résumé

This paper delves into the fundamental and versatile field of fixed point theory within functional analysis. Given its wide-ranging applications, numerous researchers have explored various generalizations and extensions of distance spaces using this theory. Our primary objective is to establish novel fixed point results for $\psi_{\mathbb{A}}$-contraction mappings in Banach spaces over $\mathbf{C}^{*}$-algebras. Our theorems unify and extend several existing results in the literature. To illustrate the practical significance of our theoretical findings, we provide illustrative examples and applications to nonlinear fractional differential equations. These applications demonstrate the versatility of our approach in solving a broad spectrum of problems.

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