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

Autor:	Samiran Mondal, Md. Rashidur Rahman, Nazmun Nahar, Md. Abdul Mannan, Halima Akter
Rok vydání:	2021
Předmět:	Pure mathematics Metric space Banach fixed-point theorem Norm (mathematics) Fixed-point theorem General Medicine Contraction principle Implicit function theorem Picard theorem Normed vector space Mathematics
Zdroj:	American Journal of Computational Mathematics. 11:157-174
ISSN:	2161-1211 2161-1203
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e533329edbd82a0d78f0f7a83f1106b9 https://doi.org/10.4236/ajcm.2021.112011 Zobrazit plný text záznamu