فاطمه شريفي

In this thesis, a novel concept called enriched contractions is introduced, an‎d their fundamental properties are investigated. This concept is a generalization of classical contraction mappings, providing broader conditions for the existence an‎d uniqueness of fixed points in metric an‎d topological spaces. By utilizing this concept, several new theorems in fixed point theory have been proven, which are considered extensions of classical theorems such as Banachʹs fixed point theorem, Brouwerʹs fixed point theorem, an‎d Karapetianʹs theorem. These results demonstrate that enriched contraction conditions can be valid for a wider class of mappings an‎d are applicable in general metric spaces, topological spaces, an‎d even more abstract spaces. Furthermore, the applications of these theorems in solving integral an‎d differential equations have been studied. We have shown how these generalizations can offer more powerful analytical tools for investigating the existence an‎d uniqueness of solutions to these equations. Finally, the obtained results are compared with existing theorems in the scientific literature, an‎d future research directions in this area are proposed.

نظريه نقطه ثابت , فضاي باناخ , عملگر پيكارد

Fixed point theory , Banach space , picard operator

Fateme Sharifi

Dr.Somayyeh Saeedi Nejad