Approximation of nonlinear operators by Volterra-Stieltjes polynomials

• Nelson Viloria Departamento de Matemáticas. Facultad de Ciencias. Universidad de Los Andes. Mérida

Keywords: nonlinear operators, polynomials operators, approximation, regulated functions, Dushnik integral

Abstract

We establish a Weierstrass approximation for operators dened in the space of regulated functions, G[a, b] , via Riesz integral representation of nonlinear operators.

References

Arbex, S. Ecuações Integrais de Volterra-Stieltjes com núcleos des-contínuos , Dr. Tese, IMEUSP, Brasil. 1976.

Baesler, I. y Daugavet, I. K. Approximation of nonlinear operators by Volterra polynomials , Amer. Math. Soc. Transl. (2), 155 (1993), 47-58.

Hönig, C. Volterra-Stieltjes Integral Equations , Math. Studies 16, North-Holland Publ. Comp., Amsterdam (1975).

Hönig, C. Équations intégrales généralisées et applications , Exp. No. 5, Publ. Math. Orsay 83, 1, Univ. Paris XI, Orsay, 1983.

Istratescu, V. Fixed Point Theory. An Introduction , volume 7. D. Reidel Publ. Comp., London, 1988.

Prandini, J. Extensions of the Representation Theorems of Riesz and Fréchet , Mathematica Bohemica, 118 (1993), 297-312.