A note on the L-fuzzy Banach’s contraction principle

2009 ◽  
Vol 41 (5) ◽  
pp. 2399-2400 ◽  
Author(s):  
J. Martínez-Moreno ◽  
A. Roldán ◽  
C. Roldán
Keyword(s):  
Contraction Principle ◽  
Banach’S Contraction Principle

Equivalent results to Banach’s contraction principle

2017 ◽  
Vol 8 (4) ◽  
pp. 435-445
Author(s):  
Maher Berzig ◽  
Cristina-Olimpia Rus ◽  
Mircea-Dan Rus
Keyword(s):  
Contraction Principle ◽  
Banach’S Contraction Principle

scholarly journals Multiple Solutions for a Sixth Order Boundary Value Problem

2021 ◽  
Vol 22 (1) ◽  
pp. 1-12
Author(s):  
A. L. M. Martinez ◽  
C. A. Pendeza Martinez ◽  
G. M. Bressan ◽  
R. M. Souza ◽  
E. W. Stiegelmeier
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Order Equation ◽  
Sixth Order ◽  
Contraction Principle ◽  
Banach’S Contraction Principle

This work presents conditions for the existence of multiple solutions for a sixth order equation with homogeneous boundary conditions using Avery Peterson's theorem. In addition, non-trivial examples are presented and a new numerical method based on the Banach's Contraction Principle is introduced.  

scholarly journals Weakly Contractive Mapping and Weakly Kannan Mapping in Partial Metric Space

2019 ◽  
Vol 20 (1) ◽  
pp. 33
Author(s):  
S. Sunarsini ◽  
S. Sadjidon ◽  
Annisa Rahmita
Keyword(s):  
Metric Space ◽  
Partial Metric Space ◽  
Contractive Mapping ◽  
Contraction Principle ◽  
Partial Metric ◽  
Weakly Contractive Mapping ◽  
Kannan Mapping ◽  
Cauchy Sequences ◽  
Weakly Contractive ◽  
Banach’S Contraction Principle

In the article the concept of metric space could be expanded, one of which is a partial metric space. In the metric space, the distance of a point to itself is equal to zero, while in the partial metric space need not be equal to zero.The concept of partial metric space is used to modify Banach's contraction principle. In this paper, we discuss weakly contractive mapping and weakly Kannan mapping which are extensions of Banach's contraction principle to partial metric space together some related examples. Additionally, we discuss someLemmas which are shows an analogy between Cauchy sequences in partial metric space with Cauchy sequences in metric space and analogy between the complete metric space and the complete partial metric space. Keywords: Cellulose metric space, partial metric space, weakly contraction mapping, weakly Kannan mapping.

scholarly journals On solutions of semilinear evolution integrodifferential equations with nonlocal conditions

2009 ◽  
Vol 40 (3) ◽  
pp. 257-269 ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations ◽  
Contraction Principle ◽  
Theory Of Evolution ◽  
Banach’S Contraction Principle

In this paper, by using the theory of evolution families, Banach's contraction principle and Schauder's fixed point theorem, we prove the existence of mild solutions of a class of semilinear evolution integrodifferential equations with nonlocal conditions in Banach space. An example is provided to illustrate the obtained results.

scholarly journals Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph

2021 ◽  
Vol 7 (1) ◽  
pp. 187-198
Author(s):  
Ana Savić ◽  
◽  
Nicola Fabiano ◽  
Nikola Mirkov ◽  
Aleksandra Sretenović ◽  
...  
Keyword(s):  
Fixed Point ◽  
Recent Work ◽  
Directed Graph ◽  
Metric Spaces ◽  
Contraction Principle ◽  
Cone Metric Spaces ◽  
Fixed Point Result ◽  
Published Paper ◽  
Banach’S Contraction Principle ◽  
Cone Metric

<abstract><p>Using the approach of so-called c-sequences introduced by the fifth author in his recent work, we give much simpler and shorter proofs of multivalued Perov's type results with respect to the ones presented in the recently published paper by M. Abbas et al. Our proofs improve, complement, unify and enrich the ones from the recent papers. Further, in the last section of this paper, we correct and generalize the well-known Perov's fixed point result. We show that this result is in fact equivalent to Banach's contraction principle.</p></abstract>

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