scholarly journals Some results on best proximity pair theorems

2002 ◽  
Vol 3 (1) ◽  
pp. 25
Author(s):  
P.S. Srinivasan ◽  
P. Veeramani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Linear Space ◽  
Point Theorem ◽  
Normed Linear Space ◽  
Sufficient Conditions ◽  
Best Proximity Pair

<p>Best proximity pair theorems are considered to expound the sufficient conditions that ensure the existence of an element x<sub>o</sub> ϵ A, such that</p> <p>d(x<sub>o</sub>; T x<sub>o</sub>) = d(A;B)</p> <p>where T : A  2<sup>B</sup> is a multifunction defined on suitable subsets A and B of a normed linear space E. The purpose of this paper is to obtain best proximity pair theorems directly without using any multivalued fixed point theorem. In fact, the well known Kakutani's fixed point theorem is obtained as a corollary to the main result of this paper.</p>

scholarly journals Schauder-Type Fixed Point Theorem in Generalized Fuzzy Normed Linear Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1643
Author(s):  
S. Chatterjee ◽  
T. Bag ◽  
Jeong-Gon Lee
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Linear Space ◽  
Present Article ◽  
Point Theorem ◽  
Normed Linear Space ◽  
Compact Operators ◽  
Linear Spaces ◽  
Basic Properties ◽  
Fuzzy Setting

In the present article, the Schauder-type fixed point theorem for the class of fuzzy continuous, as well as fuzzy compact operators is established in a fuzzy normed linear space (fnls) whose underlying t-norm is left-continuous at (1,1). In the fuzzy setting, the concept of the measure of non-compactness is introduced, and some basic properties of the measure of non-compactness are investigated. Darbo’s generalization of the Schauder-type fixed point theorem is developed for the class of ψ-set contractions. This theorem is proven by using the idea of the measure of non-compactness.

ON n-NORMED LINEAR SPACE VALUED STRONGLY (C,1)-SUMMABLE DIFFERENCE SEQUENCES

2010 ◽  
Vol 03 (04) ◽  
pp. 565-575 ◽  
Author(s):  
Hemen Dutta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Linear Space ◽  
Point Theorem ◽  
Normed Linear Space ◽  
Difference Sequences ◽  
The Fixed Point Theorem ◽  
Bounded Sequences

In this article we extend the notion of famous strongly ( C ,1)-summable or strongly Cesàro summable real sequences to n-normed linear space valued difference sequences. Consequently we introduce the notions of n-normed linear space (n-nls) valued strongly Cesàro [Formula: see text]-summable, strongly Cesàro [Formula: see text]-null and strongly Cesàro [Formula: see text]-bounded sequences. Further we extend and investigate the notion of n-norm and derived (n - l) - norms, for all l = 1, 2, …, n - 1 on the spaces of these three types of sequences. We also prove the Fixed point theorem for these spaces, which are n-Banach spaces under certain conditions and compute the n-isometrically isomorphic spaces. This article also introduces an idea for constructing n-norm on spaces of n-nls valued summable difference sequences.

scholarly journals Existence of Positive Periodic Solutions for a Class ofn-Species Competition Systems with Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Peilian Guo ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
The Fixed Point Theorem

By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class ofn-species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect.

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

On a fixed point theorem and its stochastic equivalent

1975 ◽  
Vol 12 (03) ◽  
pp. 605-611 ◽  
Author(s):  
Joseph A. Yahav
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Limiting Distribution

A discrete-time Markov process on the interval [0, 1] is considered. Sufficient conditions for the existence of a unique stationary limiting distribution are given.

scholarly journals On the controllability of fractional dynamical systems

2012 ◽  
Vol 22 (3) ◽  
pp. 523-531 ◽  
Author(s):  
Krishnan Balachandran ◽  
Jayakumar Kokila
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Matrix Function ◽  
Sufficient Conditions ◽  
Schauder’S Fixed Point Theorem ◽  
Finite Dimensional ◽  
Linear And Nonlinear ◽  
Controllability Grammian

Abstract This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

scholarly journals Multiple Positive Symmetric Solutions top-Laplacian Dynamic Equations on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-27
Author(s):  
You-Hui Su ◽  
Can-Yun Huang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Discrete Equations ◽  
Special Cases ◽  
Krasnosel’Skii’S Fixed Point Theorem

This paper makes a study on the existence of positive solution top-Laplacian dynamic equations on time scales&#x1D54B;. Some new sufficient conditions are obtained for the existence of at least single or twin positive solutions by using Krasnosel'skii's fixed point theorem and new sufficient conditions are also obtained for the existence of at least triple or arbitrary odd number positive solutions by using generalized Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem. As applications, two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.

ALMOST PERIODICITY IN AN IMPULSIVE LOGISTIC EQUATION WITH INFINITE DELAY

2008 ◽  
Vol 01 (03) ◽  
pp. 355-360 ◽  
Author(s):  
CHUNHUA FENG ◽  
ZHENKUN HUANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Logistic Equation ◽  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic

By employing a fixed point theorem in cones, this paper investigates the existence of almost periodic solutions for an impulsive logistic equation with infinite delay. A set of sufficient conditions on the existence of almost periodic solutions of the equation is obtained.

scholarly journals Null controllability of neutral evolution integrodifferential systems with infinite delay

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
K. Balachandran ◽  
A. Leelamani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Null Controllability ◽  
Neutral Evolution ◽  
Sadovskii Fixed Point Theorem

We establish a set of sufficient conditions for the controllability of nonlinear neutral evolution integrodifferential systems with infinite delay in Banach spaces. The results are established by using the Sadovskiĭ fixed point theorem and generalize the previous results.

Sign in / Sign up

Export Citation Format

Share Document