A Study of Banach Fixed Point Theorem and It’s Applications

作     者：Md. Abdul Mannan Md. R. Rahman Halima Akter Nazmun Nahar Samiran Mondal Md. Abdul Mannan;Md. R. Rahman;Halima Akter;Nazmun Nahar;Samiran Mondal

作者机构：Department of Mathematics Uttara University Dhaka Bangladesh Department of Computer Science & Engineering Prime University Dhaka Bangladesh Department of Mathematics Jashore University of Science and Technology Jashore Bangladesh 

出 版 物：《American Journal of Computational Mathematics》 (美国计算数学期刊（英文）)

年 卷 期：2021年第11卷第2期

页      面：157-174页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Metric Space Norm Space Complete Norm Space Operator Banach Fixed Point Theorem Uniformity Strong and Weak contraction Semi-Continuous 

摘      要：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.