scholarly journals WITHDRAWN: A fixed point theorem on Hilbert spaces for potential α-positively homogeneous operators via weak Ekeland variational principle

2016 ◽  
Author(s):  
M. Briki ◽  
T. Moussaoui
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Hilbert Spaces ◽  
Ekeland Variational Principle ◽  
Homogeneous Operators

scholarly journals Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓp(·)

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 375
Author(s):  
Monther R. Alfuraidan ◽  
Mohamed A. Khamsi
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Successful Treatment ◽  
Variable Exponent ◽  
Triangle Inequality ◽  
Sequence Spaces ◽  
Ekeland Variational Principle ◽  
The Core

In this work, we investigate the modular version of the Ekeland variational principle (EVP) in the context of variable exponent sequence spaces ℓ p ( · ) . The core obstacle in the development of a modular version of the EVP is the failure of the triangle inequality for the module. It is the lack of this inequality, which is indispensable in the establishment of the classical EVP, that has hitherto prevented a successful treatment of the modular case. As an application, we establish a modular version of Caristi’s fixed point theorem in ℓ p ( · ) .

scholarly journals A generalized form of Ekeland’s variational principle

2012 ◽  
Vol 20 (1) ◽  
pp. 101-112 ◽  
Author(s):  
Csaba Farkas
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Ekeland’S Variational Principle ◽  
Ekeland Variational Principle ◽  
Ekeland's Variational Principle ◽  
Common Generalization

Abstract In this paper we prove a generalized version of the Ekeland variational principle, which is a common generalization of Zhong variational principle and Borwein Preiss Variational principle. Therefore in a particular case, from this variational principle we get a Zhong type variational principle, and a Borwein-Preiss variational principle. As a consequence, we obtain a Caristi type fixed point theorem.

scholarly journals A minimization theorem in quasi-metric spaces and its applications

2002 ◽  
Vol 31 (7) ◽  
pp. 443-447 ◽  
Author(s):  
Jeong Sheok Ume
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Caristi’S Fixed Point Theorem ◽  
Caristi's Fixed Point Theorem

We prove a new minimization theorem in quasi-metric spaces, which improves the results of Takahashi (1993). Further, this theorem is used to generalize Caristi's fixed point theorem and Ekeland'sϵ-variational principle.

scholarly journals Approximate controllability of semilinear neutral systems in Hilbert spaces

2003 ◽  
Vol 16 (3) ◽  
pp. 233-242 ◽  
Author(s):  
N. I. Mahmudov ◽  
S. Zorlu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Linear Part ◽  
Schauder Fixed Point Theorem ◽  
Neutral Systems ◽  
Schauder Fixed Point ◽  
Schäuder Fixed Point Theorem

The approximate controllability of semilinear neutral systems in Hilbert spaces is studied using the Schauder fixed point theorem. It is shown that the approximate controllability of the semilinear system under some conditions is implied by the approximate controllability of its linear part.

Sign in / Sign up

Export Citation Format

Share Document