Uniformly bounded set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener

• Autorzy: Guerrero J. A. , Matkowski J. , Merentes N. , Wróbel M.

Identyfikatory

DOI

10.17512/jamcm.2015.4.05

• Języki publikacji: EN

Abstrakty

EN

We show that the one-sided regularizations of the generator of any uniformly bounded set-valued Nemytskij composition operator mapping the space of bounded variation functions in the sense of Wiener into the space of bounded variation functions with closed bounded convex values (in the sense of Wiener) are affine functions.

Słowa kluczowe

EN

ø-variation in the sense of Wiener; set-valued functions; left and right regularizations; uniformly bounded operator; composition Nemytskij operator; Jensen equation

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2015
• Tom: Vol. 14, nr 4
• Strony: 41--51
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Guerrero J. A.

• Dpto. de Matemáticas y Física, Universidad Nacional Experimental del Táchira San Cristóbal, Venezuela

autor

Matkowski J.

• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra Zielona Góra, Poland

autor

Merentes N.

• Escuela de Matemáticas, Universidad Central de Venezuela Caracas, Venezuela

autor

Wróbel M.

• Institute of Mathematics and Computer Science, Jan Długosz University Częstochowa, Poland

Bibliografia

• [1] Azócar A., Guerrero J.A., Matkowski J., Merentes N., Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener, Opuscula Mathematica 2010, 30(1), 53-60.
• [2] Matkowski J., Uniformly bounded composition operators between general Lipschitz function normed spaces, Topol. Methods. Nonlinear Aval. 2011, 38(2), 395-406.
• [3] Matkowski J., Wróbel M., Uniformly bounded set-valued Nemytskij operators acting between generalized Hölder functions spaces, Cent. Eur. J. Math. 2012, 10(2), 609-618.
• [4] Matkowski J., Wróbel M., Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder functions spaces, Discuss. Math. Differ. Incl. Control Optim. 2011, 31(2), 183-198.
• [5] Natanson I.P., Theory of Functions of a Real Variable, Nauka, Moscow 1974 (in Russian).
• [6] Wiener N., The quadratic variation of a function and its Fourier coefficients, Massachusetts J. Math. Phys. 1924, 3, 72-94.
• [7] Young L.C., Sur une généralisation de la notion de variation de puissance piéme bornée au sens de N. Wiener, et sur la convergence des séries de Fourier, C.R. Acad. Sci. 1937, 204(7), 470-472.
• [8] Musielak J., Orlicz W., On generalized variations (1), Studia Math. 1959, XVIII, 11-44.
• [9] Ciemnoczołowski J., Orlicz W., Composing functions of bounded φ-variation, Proc. Amer. Math. Soc. 1986, 96, 431-436.
• [10] Maligranda L., Orlicz W., On some properties of functions of generalized variation, Monatsh. Math. 1987, 104, 53-60.
• [11] Luxemburg W.A., Banach Function Spaces, Ph.D. Thesis, Technische Hogeschod te Deift, The Netherlands 1955.
• [12] Nakano H., Modulared Semi - Ordered spaces, Tokyo 1950.
• [13] Orlicz J.W., A note on modular spaces, I. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 1961, 9, 157-162.
• [14] Castaing C., Valadier M., Convex analysis and measurable multifunctions, Lecture Notes in Math. 1977, 580.
• [15] De Blasi F.S., On differentiability of multifunctions, Pac. J. Math. 1976, 66, 67-81.
• [16] Chistyakov V.V., Lipschitzian Nemytskii operators in the cones of mappings of bounded Wiener ψ-variation, Folia Math. 2004, 11(1), 15-39.
• [17] Smajdor W., Note on Jensen and Pexider functional equations, Demonstratio Mathematica 1999, 32, 363-376.
• [18] Matkowski J., Miś J., On a characterization of Lipschitzian operators of substitution in the space BV(a,b), Math. Nachr. 1984, 117, 155-159.
• [19] Matkowski J., Lipschitzian composition operators in some function spaces, Nonlinear Anal. 1997, 3, 719-726.
• [20] Zawadzka G., On Lipschitzian operators of substitution in the space of set-valued functions of bounded variation, Radovi Matematicki 1990, 6, 279-293
• [21] Smajdor A., Smajdor W., Jensen equation and Nemytskij operator for set-valued functions, Rad. Mat. 1989, 5, 311-320.
• [22] Matkowski J., Functional equations and Nemytskij operators, Funkc. Ekvacioj Ser. Int. 1982, 25, 127-132.