TITLE:
A Study of Banach Fixed Point Theorem and It’s Applications
AUTHORS:
Md. Abdul Mannan, Md. R. Rahman, Halima Akter, Nazmun Nahar, Samiran Mondal
KEYWORDS:
Metric Space, Norm Space, Complete Norm Space, Operator, Banach Fixed Point Theorem, Uniformity, Strong and Weak contraction, Semi-Continuous
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.11 No.2,
June
9,
2021
ABSTRACT: This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.