A Remark on the Converse of Banach's Contraction Theorem

1968 ◽  
Vol 75 (7) ◽  
pp. 775
Author(s):  
Shouro Kasahara
Keyword(s):  
Contraction Theorem

Extension of fixed point results in intuitionistic fuzzy b metric space

2020 ◽  
Vol 39 (5) ◽  
pp. 7831-7841
Author(s):  
Nabanita Konwar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Cauchy Sequence ◽  
Fixed Point Theorems ◽  
Unique Fixed Point ◽  
Intuitionistic Fuzzy ◽  
Contraction Theorem

The aim of this paper is to define the notion of intuitionistic fuzzy b metric space (in short, IFbMS) along with some useful results. We establish some important Lemmas in order to study the Cauchy sequence in IFbMS. To further develop the work, we establish some fixed point theorems and study the existence of unique fixed point of some self mappings in IFbMS. We also develop the concept of Ćirić quasi-Contraction theorem in IFbMS. Examples are provided to validate the non-triviality of the results.

Controllability results of fractional integro-differential equation with non-instantaneous impulses on time scales

2020 ◽  
Author(s):  
Vipin Kumar ◽  
Muslim Malik
Keyword(s):  
Differential Equation ◽  
Functional Analysis ◽  
Time Scales ◽  
Linear Functional ◽  
Integro Differential Equation ◽  
Numerical Example ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem ◽  
Different Time Scales

Abstract In this work, we investigate the controllability results of a fractional integro-differential equation with non-instantaneous impulses on time scales. Banach contraction theorem and the non-linear functional analysis have been used to establish these results. In support, a numerical example with simulation for different time scales is given to validate the obtained analytical outcomes.

Contraction theorem for the algebraic reduction of (anti)commutators involving operator strings

1981 ◽  
Vol 23 (4) ◽  
pp. 1632-1638 ◽  
Author(s):  
Frank E. Harris ◽  
Bogumił Jeziorski ◽  
Hendrik J. Monkhorst
Keyword(s):  
Contraction Theorem ◽  
Algebraic Reduction

Renormalisation of finitely ramified fractals

1995 ◽  
Vol 125 (5) ◽  
pp. 1085-1104 ◽  
Author(s):  
Volker Metz
Keyword(s):  
Transition Probabilities ◽  
Coarse Graining ◽  
Dirichlet Forms ◽  
Approximation Procedure ◽  
Basic Tool ◽  
Convergence Problem ◽  
Finite Graphs ◽  
Resistor Networks ◽  
Contraction Theorem ◽  
Self Similar

Transition probabilities are calculated which make the construction of diffusions on finitely ramified fractals straightforward. In contrast to former approaches using Brouwer's Fixed Point Theorem, we consider an approximation procedure based on the iteration of a nonlinear mapL. Physically, this is done by ‘coarse-graining-renormalisation of finite electric resistor networks’. Mathematically, it is a convergence problem for quotients of Dirichlet forms on finite graphs. These graphs approximate finitely ramified fractals. The basic tool is a contraction theorem for the renormalisation mapLwhich allows the use of known results about nested fractals for non-nested (p.c.f. self-similar) ones. In general, the above contraction is not strict because several linear independent fixed points occur.

scholarly journals On Some Fixed Point Results in E − Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Rachid Mecheraoui ◽  
Zoran D. Mitrović ◽  
Vahid Parvaneh ◽  
Hassen Aydi ◽  
Naeem Saleem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Additional Condition ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
New Class ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem

In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.

scholarly journals Fuzzy Meir-Keeler’s Contraction and Characterization

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Kianoush Fathi Vajargah ◽  
Hamid Mottaghi Golshan
Keyword(s):  
Contraction Theorem

In this study, a fuzzy Meir-Keeler’s contraction theorem for complete FMS based on George and Veeramani idea is established. Then, we characterize fuzzy Meir-Keeler’s contractions as contractive types induced by functions called fuzzy L -function. Moreover, we show that the converse of it is true. Finally, we bring some examples and corollaries certify our results and new improvement.

scholarly journals Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem

1999 ◽  
Vol 12 (1) ◽  
pp. 91-97 ◽  
Author(s):  
Ludwik Byszewski
Keyword(s):  
Cauchy Problem ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Special Kind ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Picard Method ◽  
Functional Differential ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Theorem

The aim of this paper is to investigate the existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem in a general Banach space. For this purpose, a special kind of a mild solution is introduced and the Banach contraction theorem and a modified Picard method are applied.

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