Fixed point theorems in generalized $C^{\ast}-$valued metric spaces

Subject Areas : Fixed point theory

H. Massit ¹ , M. Rossafi ^{2 *}

1 - Laboratory Analysis, Geometry and Applications, University of Ibn Tofail, Kenitra, Morocco
2 - Laboratory Analysis, Geometry and Applications, Higher School of Education and Training, University of Ibn Tofail, Kenitra, Morocco

Received: 2025-03-11 Accepted : 2025-04-15 Published : 2025-04-20

Keywords: Fixed point, $C^{\ast}-$valued metric space, $C^{\ast}-$valued $b-$metric space,

Abstract :

Based on the notion and properties of $C^{\ast}-$algebras, this paper aims to collect important results of fixed point theorems in generalized $C^{\ast}-$valued metric spaces. We also prove some new notions and establish an existence result for an integral equation in $C^{\ast}-$valued $b-$metric spaces. Moreover, we give some fixed point theorems in different types of spaces such as $C^{\ast}-$valued (extended $b-$metric, $b-$rectangular metric, extended hexagonal $b-$asymmetric, $S-$metric, $G-$metric and partial metric) spaces.

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