On the first and second variation in the sense of Schramm-Riesz

Authors

  • Mireya Bracamonte Universidad Centroccidental Lisandro Alvarado, Venezuela
  • José Gimenez Universidad de Los Andes, Venezuela
  • Nelson Merentes Universidad Central de Venezuela, Venezuela

Keywords:

Variation of a Function, N-Function, N-sequence

Abstract

In this paper we present a generalization of the concepts of first and second F-variation (where F is a certain sequence of positive convex function defined on [0;+8], in the sense of Schramm-Riesz for normed space valued functions defined on an interval [a;b] c R. We characterized the functions of second F- variation in the sense of Schramm-Riesz, as those that can be expressed as the integral of a function of bounded F-variation in the sense of Schramm-Riesz.

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Author Biographies

Mireya Bracamonte, Universidad Centroccidental Lisandro Alvarado, Venezuela

Decanato de Ciencias y Tecnología, Departamento de Matemáticas

José Gimenez, Universidad de Los Andes, Venezuela

Departamento de Matemáticas

Nelson Merentes, Universidad Central de Venezuela, Venezuela

Escuela de Matemáticas

References

V. Barbu and Th. Precupanu. (1978). Convexity and Optimization on Banach Spaces. Sijthof and Noordho, the Nederlands,
M. Bracamonte, J. Giménez, N. Merentes and J. Sánchez. On second Riesz F- variation of normed space valued maps, Advances in Pure Mathematics, 2, No. 1, 45-58. (2012).
D. Bugajewska. On the superposition operator in the space of functions of bounded variation, revisted. Mathematical and Computer Modelling 52(5-6). 791- 796 (2010).
V. V. Chistyakov. Mappings of generalized variation and composition operators. J. Math. Sci. 11, 2455 - 2466(2002).
Z. Cybertowicz and W. Matuszewska. Functions of bounded generalized variations, Comment. Math. Prace Mat. 20, No. 1, 29-52 (1977).
J. Giménez, N. Merentes and S. Rivas. Integral Representation of functions of bounded second F-variation in the sense of Schramm. Opuscula Mathematica, Vol 32, No 1, 137-151 (2012).
C. Jordan. Sur la serie de Fourier, C. R. Acad. Sci. Paris, 228-230, 2 (1881).
Ch. J. De la Vallee Poussin. Sur la convergence des formules d'interpolation entre ordennees equidistantes, Bull. Acad. Sei. Belg. 314-410 (1908).
T. Ereu, N. Merentes and J. L. Sánchez. Some remarks on the algebra of functions of two variables with bounded total F-variation in Schramm sense. Commentationes Mathematicae (2010).
T. Ereu, N. Merentes, B. Rzepka, J. Sánchez. On composition operator in the algebra of functions of two variables with bounded total F- variation in Schramm sense. Journal of Mathematics and Applications. No 33, pp 35-50 (2010).
T. Ereu, N. Merentes, J. Sánchez, and M. Wrobel. Uniformly continuous composition operators in the space of bounded Phi-variation functions in Schramm sense. Opuscula Mathematica.
L. Maligranda. Orlicz Spaces and Interpolation, Seminars in Math. 5, University of Campinas, IMECC-UNICAMP, Brasil, (1989).
Yu. T. Medvedev. Generalization of a theorem of F. Riesz, Uspehi Matem. Nauk (N.S.) 8 (1953), No. 6(58), 115-118 (Russian).
J. Musielak and W. Orlicz. On modular spaces, Studia Math. 18 (1959), 49-65.
J. Musielak. Orlicz Spaces and Modular Spaces, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, (1983).
F. Riesz. Sur certains systems singuliers d'equations integrates, Annales de L'Ecole Norm. Sup., Paris, (3) 28, 33-68 (1911).
M. Russell and C. J. F. Upton. A generalization of a theorem by F. Riesz, Analysis Math, 9 (1983), 69-77.
M. Schramm. Functions of F-bounded variation and Riemann-Stieltjes integration, Trans. Amer. Math. Soc. 287, 49-63(1985).
L. C. Young. Sur une generalisation de la notion de variation de pussance pieme bornee au sens de M. Wiener, et sur la convergence des series de Fourier, C. R. Acad. Sci. Paris, 204, Ser A-B, 470-472 (1937).

Published

2013-06-19

How to Cite

[1]
M. Bracamonte, J. Gimenez, and N. Merentes, “On the first and second variation in the sense of Schramm-Riesz”, Publ.Cienc.Tecnol, vol. 7, no. 1, pp. 37-50, Jun. 2013.

Issue

Section

Research Article