An investigation of the fixed point analysis and practices
An In-Depth Guide to Fixed-Point Theorems, NOVA Publications , ss.203-245, 2021
- Yayın Türü: Kitapta Bölüm / Araştırma Kitabı
- Basım Tarihi: 2021
- Yayınevi: NOVA Publications
- Sayfa Sayıları: ss.203-245
- Kırklareli Üniversitesi Adresli: Evet
Özet
The concept of metric spaces and the related fixed point theorems are of utmost importance in the field of functional analysis. It acts as a major tool to workout the solutions on the problems related to optimization, approximation theory, operator theory, quantum physics, engineering, dynamical systems, computer sciences and other branches of applied mathematics. In 1922, Stefan Banach, a polish mathematician, constructed a result famously known as "Banach's fixed point theorem" or "Banach contraction principle" which acts as a benchmark in an area of Fixed Point Theroy and its Applications. Thereafter, Fixed point Theory paves a way to many interesting and attractive results in different metric spaces and finds its applications to many real life situations. In this book chapter, we begin with some basic notations, definitions, propositions and theorems considering complete metric spaces such as G- metric, s-metric, b-metric, C - metric space, cone metric, d- metric and so on. Then, we define some fixed point theorems in the such spaces. Besides, we recognize a notation called as C*-algebra defined recently and several types of C*-algebra valued metric space with theories. Finally, we present a fixed point result on the C*-algebra valued b- metric space. An application to differential and integral equations is also provided.