شذي ال جياد

This dissertation explores the concept of fuzzy b-metric spaces, which serve as a generalization of both fuzzy metric spaces an‎d b-metric spaces. The Banach contraction principle is extended to the framework of fuzzy b-metric spaces, supported by a detailed illustrative example. The notion of g-orbitally upper semi-continuous functions is introduced within fuzzy metric spaces, leading to a generalization of the fixed point theorem originally proposed by Hicks an‎d Rhoads in the setting of fuzzy b-metric spaces. Several fixed point theorems are established using a newly proposed rational contraction condition an‎d a control function, specifically within the fuzzy b-metric space framework. Applications resulting from these theorems are also presented. These concepts are further utilized to derive new fixed point an‎d common fixed point results for Geraghty-type contractions in G-complete fuzzy b-metric spaces. In addition, the study introduces the concept of a generalized fuzzy metric space, which encompasses an‎d extends various topological structures such as fuzzy metric spaces, fuzzy b-metric spaces, an‎d dislocated fuzzy metric spaces. It is demonstrated that the class of generalized fuzzy metric spaces properly includes the aforementioned spaces as subclasses. Furthermore, the Banach contraction principle an‎d Cirić’s quasi-contraction theorem are established within this generalized framework. As consequences, several recent results, including those by Jleli an‎d Samet, are obtained as corollaries. An application to a nonlinear integral equation is also discussed to illustrate the practical implications of the main theoretical findings.

فضاي فازي b-متريك , ؛ اصل انقباض باناخ , تابع g-مداري نيمه‌پيوسته از بالا , قضيه نقطه ثابت

Fuzzy b-metric space. , g-orbitally upper semi- continuous function , fixed point theorem , Banach contraction principle

SHATHA AL CHYAD

Reza Saadati