Corrigendum to "\eta-admissible mappings in C^*-algebra-valued \mathcal{MP}-metric spaces with an application"

This article is a revision and correction of the chapter book [S. Hadi Bonab, V. Parvaneh, Z. Bagheri, \eta_{\mathcal{A}}-Admissible Mappings for Four Maps in C*-Algebra-Valued MP-Metric Spaces with an Application, In: P. Debnath, Delfim F. M. Torres, Yeol Je Cho, Advanced Mathematical Analysis and its Applications, CRC Press, ۲۰۲۳, ۹۷-۱۱۳.]. In this article, we first introduce the concept of \eta-admissible mapping in C^*-algebra valued \mathcal{MP}-metric spaces, which is a generalization and combination of "modular metric spaces", "parametric metric spaces" and "C^*-algebra-valued metric spaces". Then, for four mappings in these spaces, we prove several fixed-point theorems. We give an example and an application regarding the solvability of operator equations and integral equations, respectively, to support the new findings.

Keywords:

metric space , parametric metric space , modular metric space , \eta-admissible mappings , C^*-algebra-valued metric space , C^*-algebra-valued \mathcal{MP}-metric space