scholarly journals Global Dynamical Systems Involving Generalized -Projection Operators and Set-Valued Perturbation in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yun-zhi Zou ◽  
Xi Li ◽  
Nan-jing Huang ◽  
Chang-yin Sun
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Banach Spaces ◽  
Equilibrium Points ◽  
Projection Operators ◽  
Initial Value ◽  
New Class ◽  
The Fixed Point Theorem ◽  
Generalized Projection Operators ◽  
Generalized Dynamical Systems

A new class of generalized dynamical systems involving generalizedf-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.

scholarly journals The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

scholarly journals Existence results for second order functional differential and integrodifferential inclusions in Banach spaces

2001 ◽  
Vol 32 (4) ◽  
pp. 315-325
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Second Order ◽  
Initial Value ◽  
Functional Differential ◽  
Condensing Maps

In this paper we investigate the existence of solutions on a compact interval to second order initial value problems for functional differential and integrodifferential inclusions in Banach spaces. We shall make use of a fixed point theorem for condensing maps due to Martelli.

scholarly journals Fixed points and their approximation in Banach spaces for certain commuting mappings

1982 ◽  
Vol 23 (1) ◽  
pp. 1-6
Author(s):  
M. S. Khan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Contraction Mappings ◽  
Continuous Mappings ◽  
Banach Contraction ◽  
The Fixed Point Theorem

1. Let X be a Banach space. Then a self-mapping A of X is said to be nonexpansive provided that ‖AX − Ay‖≤‖X − y‖ holds for all x, y ∈ X. The class of nonexpansive mappings includes contraction mappings and is properly contained in the class of all continuous mappings. Keeping in view the fixed point theorems known for contraction mappings (e.g. Banach Contraction Principle) and also for continuous mappings (e.g. those of Brouwer, Schauderand Tychonoff), it seems desirable to obtain fixed point theorems for nonexpansive mappings defined on subsets with conditions weaker than compactness and convexity. Hypotheses of compactness was relaxed byBrowder [2] and Kirk [9] whereas Dotson [3] was able to relax both convexity and compactness by using the notion of so-called star-shaped subsets of a Banach space. On the other hand, Goebel and Zlotkiewicz [5] observed that the same result of Browder [2] canbe extended to mappings with nonexpansive iterates. In [6], Goebel-Kirk-Shimi obtainedfixed point theorems for a new class of mappings which is much wider than those of nonexpansive mappings, and mappings studied by Kannan [8]. More recently, Shimi [12] used the fixed point theorem of Goebel-Kirk-Shimi [6] to discuss results for approximating fixed points in Banach spaces.

Existence Results on Infinite Intervals for Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces

2000 ◽  
Vol 7 (4) ◽  
pp. 609-625 ◽  
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas
Keyword(s):  
Banach Spaces ◽  
Initial Value Problems ◽  
Mild Solutions ◽  
Existence Results ◽  
Topological Spaces ◽  
Initial Value ◽  
Infinite Intervals ◽  
Functional Differential ◽  
The Fixed Point Theorem ◽  
Locally Convex

Abstract In this paper we investigate the existence of mild solutions, on infinite intervals, to initial value problems for neutral functional differential and integrodifferential inclusions in Banach spaces. We shall rely on the fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem.

scholarly journals A proximal point method for nonsmooth convex optimization problems in Banach spaces

1997 ◽  
Vol 2 (1-2) ◽  
pp. 97-120 ◽  
Author(s):  
Y. I. Alber ◽  
R. S. Burachik ◽  
A. N. Iusem
Keyword(s):  
Banach Space ◽  
Convex Optimization ◽  
Banach Spaces ◽  
Optimization Problems ◽  
Geometric Characteristic ◽  
Point Method ◽  
Proximal Point Method ◽  
Projection Operators ◽  
Proximal Point ◽  
Generalized Projection Operators

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.

Controllability of Sobolev Type Semilinear Functional Differential and Integrodifferential Inclusions with an Unbounded Delay

2006 ◽  
Vol 13 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Yong-Kui Chang ◽  
Wan-Tong Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Unbounded Delay ◽  
Functional Differential ◽  
The Fixed Point Theorem ◽  
Condensing Maps

Abstract In this paper, sufficient conditions are established for the controllability of Sobolev type semilinear functional differential and integrodifferential inclusions with an unbounded delay in Banach spaces. The main results are obtained by using the fixed point theorem for condensing maps due to Martelli.

scholarly journals Brzdęk’s fixed point method for the generalised hyperstability of bi-Jensen functional equation in (2,β)-Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4897-4910
Author(s):  
Iz-Iddine El-Fassi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Point Method ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
The Fixed Point Theorem

Using the fixed point theorem [12, Theorem 1] in (2,?)-Banach spaces, we prove the generalized hyperstability results of the bi-Jensen functional equation 4f(x + z/2; y + w/2) = f (x,y) + f (x,w) + f (z,y) + f (y,w). Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. The method we use here can be applied to various similar equations in many variables.

scholarly journals Stability of Fuzzy Dynamical Systems via Lyapunov Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Abdelati El Allaoui ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Dynamical Systems ◽  
Initial Value Problems ◽  
Lyapunov Functions ◽  
Equilibrium Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Initial Value ◽  
Necessary And Sufficient ◽  
Fuzzy Dynamical Systems

The purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterization of stability by a study of the trajectories of fuzzy dynamical systems, using auxiliary functions, and they will be called fuzzy Lyapunov functions. And, among the main results that have been proven is that the existence of fuzzy Lyapunov functions is a necessary and sufficient condition for stability. Some examples are given to illustrate the obtained results.

scholarly journals Iterating nonlinear contractive mappings in Banach spaces

2020 ◽  
Vol 36 (2) ◽  
pp. 287-294
Author(s):  
ZORAN D. MITROVIC ◽  
◽  
STOJAN RADENOVIC ◽  
SIMEON REICH ◽  
ALEXANDER J. ZASLAVSKI ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
New Class ◽  
Contractive Mappings

We introduce a new class of nonlinear contractive mappings in Banach spaces, study their iterates and establish a fixed point theorem for them.

scholarly journals On Existence and uniqueness to solutions nonlocal integrodifferential equations

2018 ◽  
Vol 1 (25) ◽  
pp. 493-508
Author(s):  
Fawzi Mutter Ismaael
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Necessary Conditions ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem

The Study aims in this paper to give and investigate the existence and uniqueness of mild solutions to nonlinear functional integrodifferential equations in Banach Spaces. the fixed point theorem, according to Sadovskii and sutible necessary conditions, are concepts consulted to obtain the results in the work

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