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Approximation of vector-valued functions by polynomials with coefficients in normed spaces applications

Anastassiou G., Gal S.

Demonstratio Mathematica

2006

Vol. 39, nr 3

539-552

In this paper we prove basic results in the approximation of vector-valued functions by polynomials with coefficients in normed spaces, called generalized polynomials. Thus we obtain : estimates in terms of Ditzian-Totik Lp-moduli of smoothness for approximation by Bernstein-Kantorovich generalized polynomials and by other kinds of operators like the Szasz-Mirakian operators, Baskakov operators, Post-Widder operators and their Kantorovich analogues and inverse theorems for these operators. Applications to approximation of random functions and of fuzzy-number-valued functions are given.

Multiobjective programming with (p, r)-invexity

Antczak T.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2001

z. 25 [190]

31-46

A nonlinear multiobjective programming problem is considered where the functions involved are differentiable. In this work, we generalize some scalar optimization theory results making them applicable to vectorial optimization. By using the concept of (p, r)-invexity we give a new characterization of solutions of multiobjective programming problems. To do this, we introduce the definitions of stationary points and Kuhn-Tucker points for multiobjective programming problems. We prove, for unconstrained multiobjective programming problems with (p,r)-invex functions, that the equivalence between optimal solutions and stationary points remains true when several objective functions are optimized instead of one objective function. Moreover, we give two types of Kuhn-Tucker optimality conditions for constrained multiobjective programming problems. For this purpose, we generalize Martin's [16] definition of KT-invex problems to vectorial optimization problems with (p,r)-invex functions.

Fractional programming with (p,r)-invexity

Antczak T.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2001

z. 25 [190]

5-29

The notion of (p, r)-invexity for a vector function is introduced and discussed its application to a class of fractional problems. Parametric and non-parametric necessary and sufficient optimality conditions and duality results for a generalized fractional programming are obtained under an appropriate (p,r)-invexity assumption on involving functions.