Notes on fixed point results of C*-algebra-valued metric spaces

Ahmad, Zulaihatu Tijjani; Shehu Shagari, Mohammed; Tijjani, Abba Ali

doi:10.30495/maca.2025.2061014.1138

Notes on fixed point results of C*-algebra-valued metric spaces

10.30495/maca.2025.2061014.1138

Volume 7, Issue 3
Summer 2025

Pages 13-65

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Zulaihatu Tijjani Ahmad

Mohammed Shehu Shagari

Abba Ali Tijjani

Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria

Abstract

It is well-known that $C^{*}$-algebra has been applied in understanding the physics of several phenomena in quantum theory, statistical mechanics and more than a handful of other domains. In continuation of these roles of $C^{*}$-algebra, its notion has recently been incorporated in metric fixed point theory, and several results have been obtained thereof. However, in accordance with the existing literature, it is revealed that a collective and comparative analysis of the announced concepts of $C^*$-algebra-valued metric spaces and the associated invariant point theorems has not been considered. One of the uses of such analysis is that it gives researchers handy information to know what has been done and the available gaps in the corresponding notions. With this background orientation, the objective of this paper is twofold: first, important developments of the idea of $C^*$-algebra-valued metric spaces are surveyed. Thereafter, a comparative analysis of possible combinations and deductions based on the already obtained results is conducted. To achieve the latter objective, a few new results are formulated and non-trivial examples constructed, where necessary, to validate some of our observations.

Keywords

C*-algebra

C*-algebra-valued metric space

fixed point

contractive mapping

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