SOME FIXED POINT THEORY RESULTS FOR CONVEX CONTRACTION MAPPING OF ORDER 2

2018 ◽  
Vol 12 (2-3) ◽  
pp. 81-130 ◽  
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theory ◽  
Point Theory

scholarly journals LMI-Based Stability Criterion for Impulsive CGNNs via Fixed Point Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xiongrui Wang ◽  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contraction Mapping Theorem ◽  
Related Literature ◽  
Variation Range ◽  
Exponentially Stable ◽  
The Stability ◽  
First Time

Linear matrices inequalities (LMIs) method and the contraction mapping theorem were employed to prove the existence of globally exponentially stable trivial solution for impulsive Cohen-Grossberg neural networks (CGNNs). It is worth mentioning that it is the first time to use the contraction mapping theorem to prove the stability for CGNNs while only the Leray-Schauder fixed point theorem was applied in previous related literature. An example is given to illustrate the effectiveness of the proposed methods due to the large allowable variation range of impulse.

A Study on Fixed Point Theory in M-Metric Space

2020 ◽  
Vol 13 (13) ◽  
pp. 62-68
Author(s):  
Prakash Muni Bajracharya ◽  
Nabaraj Adhikari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Partial Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
The Fixed Point Theorem

In 2014, Asadi et al.1 introduced the notion of an M−metric space which is the generalization of a partial metric space and establish Banach and Kannan fixed point theorems in M− metric space. In this paper, we give a brief survey regarding the fixed point theorem for Chatterjea contraction mapping in the framework of M−metric space. We also give some examples which support the partial answers to the question posed by Asadi et al. concerning a fixed point for Chatterjea contraction mapping.

scholarly journals Fixed point results for Ciric typeweak contraction in metric spaces with applications to partial metric spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1505-1516 ◽  
Author(s):  
Binayak Choudhury ◽  
A. Kundu ◽  
N. Metiya
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
Weak Contraction ◽  
Control Functions ◽  
Partial Metric Spaces

Partial metric spaces are generalizations of metric spaces which allow for non-zero self-distances. The need for such a definition was felt in the domain of computer science. Fixed point theory has rapidly developed on this space in recent times. Here we define a Ciric type weak contraction mapping with the help of discontinuous control functions and show that in a complete metric space such a function has a fixed point. Our main result has several corollaries and is supported with examples. One of the examples shows that the corollaries are properly contained in the theorem. We give applications of our results in partial metric spaces.

scholarly journals Existence of Fixed Point Under Generalized Multivalued - -Contraction in Partial Metric Spaces

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Smita Negi ◽  
Umesh Chandra Gairola
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Partial Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
Multivalued Contraction ◽  
Partial Metric Spaces

In this paper, we introduce the notion of generalized multivalued - -contraction in partial metric space endowed with an arbitrary binary relation and establish a fixed point theorem for this contraction mapping. Our result extends and generalize the result of Wardowski (Fixed Point Theory Appl. 2012:94 (2012)), Alam and Imdad (J. Fixed Point Theory Appl. 17 (4) (2015), 693–702) and Altun et al. (J. Nonlinear Convex Anal. 28 (16) (2015), 659-666). Also, we give an example to validate our result.

Comments on some fixed point theorems in metric spaces

2018 ◽  
Vol 27 (1) ◽  
pp. 15-20
Author(s):  
VASILE BERINDE ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contraction Mapping Principle ◽  
Contraction Condition

In a recent paper [Pata, V., A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), No. 2, 299–305], the author stated and proved a fixed point theorem that is intended to generalize the well known Banach’s contraction mapping principle. In this note we show that the main result in the above paper does not hold at least in two extremal cases for the parameter ε involved in the contraction condition used there. We also present some illustrative examples and related results.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

scholarly journals A new method in fixed point theory

1960 ◽  
Vol 34 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Richard G. Swan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Method
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