Wyniki wyszukiwania - BazTech

1

On a certain property of generalized Hölder functions

Lupa M.

Journal of Applied Mathematics and Computational Mechanics

|

2015

|

Vol. 14, nr 4

127--132

EN

In this paper some properties of functions belonging to the space Wy[a,b] of generalized Hölder functions are considered. These functions are r-times differentiable and their r-th derivatives satisfy the generalized Hölder condition. The main result of the paper is a proof of the fundamental lemma that the recursive model-defined functions ℎk: I × Rk+1 → R, k = 0,1, … , r are a special form and belong to the space Wy[a,b].

2

A special case of generalized Hölder functions

Lupa M.

Journal of Applied Mathematics and Computational Mechanics

|

2014

|

Vol. 13, nr 4

81--89

EN

In this paper some properties of a special case of generalized Hölder functions, which belong to the space W γ [a, b], are considered. These functions are r-times differentiable and their r-th derivatives satisfy the generalized Hölder condition. The main result of the paper is a proof of the theorem that product of two functions belonging to the space W γ [a, b] also belongs to this space.

3

Some convergence results for nonlinear singular integral operators

Karsli H.

Demonstratio Mathematica

|

2013

|

Vol. 46, nr 4

729--740

EN

In this paper, we establish some pointwise convergence results for a family of certain nonlinear singular integral operators Tλf of the form (...), acting on functions with bounded (Jordan) variation on an interval [a, b] as λ→λ0. Here, the kernels (...) satisfy some suitable singularity assumptions. We remark that the present study is a continuation and extension of the study of pointwise approximation of the family of nonlinear singular integral operators (1) begun in [18].

4

Rotative mappings in metric spaces of hyperbolic type

Górnicki J., Pupka K.

Journal of Mathematics and Applications

|

2006

|

Vol. 28

49-70

EN

The aim of this paper is to give some conditions providing existence of fixed points for k-lipschitzian and uniformly k-lipschitzian mappings which are n-rotative with n ≥ 2 in complete metric spaces of hyperbolic type.

5

Time-parametric control : uniform convergence of the optimal value functions of discretized problems

Gugat M.

Control and Cybernetics

|

1999

|

Vol. 28, no 1

7-33

EN

The problem of time-optimal control of linear hyperbolic systems is equivalent to the computation of the root of the optimal value function of a time-parametric program, whose feasible set is described by a countable system of moment equations. To compute this root, discretized problems with a finite number of equality constraints can be used. In this paper, we show that on a certain time-interval, the optimal value functions of the discretized problems converge uniformly to the optimal value function of the original problem. We also give sufficient conditions fot Lipschitz and Hoelder continuity of the optimal value function of the original problem.

6

On random Lipschitz condition and its application in approximation theory

Musielak J.

Fasciculi Mathematici

|

1998

|

Nr 28

119-125

EN

There are estimated moduli of continuity of functions satisfying Lipschitz condition with random exponents both in the sense of convergence in probability and convergence in mean. The results are applied to extend Jackson's direct approximation theorem to the case of Lipschitz condition with a random exponent.