Author(s)

Md. Abdul Mannan^1*, Md. R. Rahman², Halima Akter¹, Nazmun Nahar¹, Samiran Mondal³

¹Department of Mathematics, Uttara University, Dhaka, Bangladesh.
²Department of Computer Science & Engineering, Prime University, Dhaka, Bangladesh.
³Department of Mathematics, Jashore University of Science and Technology, Jashore, Bangladesh.

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.

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

Mannan, M. , Rahman, M. , Akter, H. , Nahar, N. and Mondal, S. (2021) A Study of Banach Fixed Point Theorem and It’s Applications. American Journal of Computational Mathematics, 11, 157-174. doi: 10.4236/ajcm.2021.112011.