Thus, T defined in 18 is an example which satisfies the given condition Banach contration theorem but have no fixed point. Thus, defined in 19 is an example which satisfies the given condition Banach contration theorem but have no fixed point. The Banach theorem seems somewhat limited. It seems intuitively clear that any continuous function mapping the unit interval into itself has a fixed point. We hope that this work will be useful for functional analysis related to normed spaces and fixed point theory.
Our results are generalizations of the corresponding known fixed point results in the setting of Banach spaces on its norm spaces. Then all expected results in this paper will help us to understand better solution of complicated theorem. In future, we will discuss of Banach spaces on its norm spaces related properties to physical problem.
I would like to thank my respectable teacher Prof. Moqbul Hossain for encouragement and valuable suggestions. Journal of Mathematical Analysis and Applications, 47, Bulletin of the American Mathematical Society, 1, Academic Press-Elsevier, London. Creative Mathematics Informatics, 21, Journal of Fixed Point Theory and Applications, 21, Journal of Nonlinear Sciences and Applications, 5, Journal of Inequalities and Applications, , Article No. International Journal of Academic Research, 3, Journal of Fixed Point Theory and Applications, 2, Home Journals Article.
DOI: Abstract This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. Share and Cite:. Mannan, M. American Journal of Computational Mathematics , 11 , Introduction It is conventional to this work motivated by some recent work on Banach fixed point theorem for mappings defined on metric spaces with a partial order or a graph. Preliminaries We will discuss Banach fixed point theorem in metric spaces with complete normed spaces and related topics.
Example Every Banach space is a normed, but the converse, in general, is not true. Banach Contraction Theorem or Principle [11] Here we will give the proof of Banach contraction theorem or principle both for metric space and normed space separately. Conclusion The Banach theorem seems somewhat limited. Acknowledgements I would like to thank my respectable teacher Prof. Conflicts of Interest The authors declare that they have no competing interests.
References [ 1 ] Ekeland, I. Journals Menu. Contact us. All Rights Reserved. Ekeland, I. Alfuraidan, M. Guran, L. Hasanzade Asl, J.
Khojasteh, F. Rudin, W. Agarwal, R. Lu, N. Best Impact Fa A short summary of this paper. Volume 10, Issue 6 Ver. III Nov - Dec. Shukla1 and Vivek Tiwari2 Deptt. Science college Rewa M. Abstract: In this paper we presents some theorems in 2 Banach spaces. Mathematics subject classification: 47H10, 54H Introduction: A large variety of the problems of analysis and applied mathematics reduce to finding solutions of non linear functional equations which can be formulated in terms of finding the fixed points of a non linear mapping.
Fixed point theorems are very important tools for proving the existence and uniqness of the solutions to various differential, integral and partial differential equations and variational inequalities etc. Ghalar [4] introduced the concept of 2- Banach. In present paper we prove some fixed point theorems for non-contraction mappings, in 2-Banach spaces motivated by above, before starting the main result first we write some definitions II.
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