Wyniki wyszukiwania - BazTech

1

On K-superquadratic set-valued functions

Troczka-Pawelec K.

Journal of Applied Mathematics and Computational Mechanics

|

2015

|

Vol. 14, nr 1

101--109

EN

In this paper we consider K-superquadratic set-valued functions. We will present here some connections between K-boundedness of K-superquadratic set-valued functions and K-semicontinuity of multifunctions of this kind.

2

K-continuity problem of K-superquadratic set-valued functions

Troczka-Pawelec K.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

|

2014

|

Vol. 19

227--235

EN

In this paper we study K-superquadratic set-valued functions.We will present here some connections between K-boundedness of K-superquadratic set-valued functions and K-semicontinuity of multifunctions of this kind.

3

K-continuity of K-subquadratic set-valued functions

Troczka-Pawelec K., Tyrala I.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

|

2014

|

Vol. 19

237--244

EN

Let X = (X, +) be an arbitrary topological group. A set-valued function F : X → n(Y) is called K-subquadratic if 2F(s) + 2F(t) ⊂ F(s + t) + F(s - t) + K, for all s, t ϵ X, where Y denotes a topological vector space and where K is a cone in this space. In this paper the K-continuity problem of multifunctions of this kind will be considered with respect to weakly K-boundedness. The case where Y = R N will be considered separately.

4

On Nemytskij operator in the space of absolutely continuous set-valued functions

Ludew J. J.

Journal of Applied Analysis

|

2011

|

Vol. 17, nr 2

277-290

EN

We consider the Nemytskij operator, defined by (Nφ)(x) ? G(x, φ(x)), where G is a given set-valued function. It is shown that if N maps AC(I, C), the space of all absolutely continuous functions on the interval I ? [0, 1] with values in a cone C in a reflexive Banach space, into AC(I, K), the space of all absolutely continuous set-valued functions on I with values in the set K, consisting of all compact intervals (including degenerate ones) on the real line R, and N is uniformly continuous, then the generator G is of the form G(x, y) = A(x)(y) + B(x), where the function A(x) is additive and uniformly continuous for every x ∈ I and, moreover, the functions x ? A(x)(y) and B are absolutely continuous. Moreover, a condition, under which the Nemytskij operator maps the space AC(I, C) into AC(I, K) and is Lipschitzian, is given.

5

Differential calculus for complex-valued multifunctions

Avelin J.

Journal of Applied Analysis

|

2000

|

Vol. 6, nr 1

47-75

EN

Using the concept of the normal cone to a multifunction we define a derivative for a complex-valued multifunction of one complex variable being a natural generalization of the ordinary complex derivative for holomorphic functions. Using results obtined by Mordukhovich, we develop a full calculus and discuss openness and Lipschitzian properties. We also prove the fundamental theorem of calculus and the Taylor expansion formula. Finally we discuss analyticity of multifunctions in the context of the normal cone.