Wyniki wyszukiwania - BazTech

1

On the Existence of Solutions of Some Stochastic Functional Integral Equations

Pasławska-Południak M.

Commentationes Mathematicae

|

2010

|

Vol. 50, [Z] 1

49-60

EN

The integral equation of Urysohn type is considered, for the deterministic and stochastic cases . We show, using the fixed point theorem of Darbo type that under some assumptions the equations have solutions belonging to the space of continuous functions. The main tool used in our paper is the technique associated with measures of noncompactness.

2

Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay

Gomaa A,M

Commentationes Mathematicae

|

2008

|

Vol. 48, [Z] 1

45-58

EN

We consider the problem [formula] in a Banach space E, where belongs to the Banach space, CE([-d, 0]), of all continuous functions from [-d, 0] into E. A multifunction F from [0, b] × CE([-d, 0]) into the set, Pfc(E), of all nonempty closed convex subsets of E is weakly sequentially hemi-continuous, tx(s) = x(t + s) for all s 2 [-d, 0] and {A(t) : 0 6 t 6 b} is a family of densely defined closed linear operators generating a continuous evolution operator S(t, s). Under a generalization of the compactness assumptions, we prove an existence result and give some topological properties of our solution sets that generalizes earlier theorems by Papageorgiou, Rolewicz, Deimling, Frankowska and Cichon..

3

On theorems for weak solutions of nonlinear differential equations with and without delay in Banach spaces

Gomaa A,M

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

|

2007

|

Vol. 47, [Z] 2

179-191

EN

In the present work we give an existence theorem for bounded weak solution of the differential equation.......[formuła matematyczna]

4

On an operator functional equation in L1 [0, ∞) and Volterra-Fredholm type integral equations

El-Sayed A. M. A., Sherif N., El-Farag I. A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

|

2003

|

[Z] 43(1)

61-76

EN

The existence of a solution of a nonlinear operator functional equation in the class of monotonic functions on the interval R+ = [0, oo) is investigated. The approach to establish the main result is based on the notion of measure of noncompactness and an associated fixed point theorem due to Darbo. A Volterra-Fredholm type integral equation arises as a particular case of the investigated nonlinear operator functional equation.

5

Convexity induced by a set quantity

Falcon S., Sadarangani K.B.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

|

2000

|

[Z] 40

57-67

EN

In the geometry of Banach spaces the notion of convexity plays a very significant role and is frequently used in many branches of functional analysis. In the last few years, there have appeared some papers containing generalizations of the concept of convexity using the notion of a measure of noncompactness. The aim of this paper is to generalize the notion of convexity using the notion of a set quantity wich has been considered in. It is worthwhile mentioning that several results obtained in the geometry involving compactness conditions have counterparts in the geometry induced by a set quantity. Particularly, we introduce a modulus related to a set quantity and we obtain a generalization of a result due to Rolewicz. Moreover, we calculate this modulus for the De Blasi measures of weak noncompactness in some classics Banach spaces such as C_0, l^1, L^1 and the James space J.