A Study of Banach Fixed Point Theorem and It’s Applications
Open Access
- 1 January 2021
- journal article
- research article
- Published by Scientific Research Publishing, Inc. in American Journal of Computational Mathematics
- Vol. 11 (02), 157-174
- https://doi.org/10.4236/ajcm.2021.112011
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.Keywords
This publication has 12 references indexed in Scilit:
- Some applications of Caristi’s fixed point theorem in metric spacesFixed Point Theory and Applications, 2016
- PrefacePublished by Elsevier BV ,2016
- A new generalization of the Banach contraction principleJournal of Inequalities and Applications, 2014
- -Metric Space: A GeneralizationMathematical Problems in Engineering, 2013
- On fixed points of α-ψ-contractive multifunctionsFixed Point Theory and Applications, 2012
- On Banach contraction principle in a cone metric spaceJournal of Nonlinear Sciences and Applications, 2012
- Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral EquationsAbstract and Applied Analysis, 2012
- A simple proof of the Banach contraction principleJournal of Fixed Point Theory and Applications, 2007
- Nonconvex minimization problemsBulletin of the American Mathematical Society, 1979
- On the variational principleJournal of Mathematical Analysis and Applications, 1974