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Warianty tytułu
Języki publikacji
Abstrakty
Some conditions under which any subadditive function is periodic are presented. It is shown that the boundedness from below in a neighborhood of a point of a subadditive periodic (s.p.) function implies its nonnegativity, and the boundedness from above in a neighborhood of a point implies it nonnegativity and global boundedness from above. A necessary and sufficient condition for existence of a subadditive periodic extension of a function ƒ0 : [0, 1) ? R is given. The continuity, differentiability of a s.p. function is discussed, and an example of a continuous nowhere differentiable s.p. function is presented. The functions which are the sums of linear functions and s.p. functions are characterized. The refinements of some known results on the continuity of subadditive functions are presented.
Czasopismo
Rocznik
Tom
Strony
75--96
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- University of Zielona Góra Faculty of Mathematics, Computer Science and Econometry ul. Szafrana 4a, 65-516 Zielona Góra, Poland Silesian University Institute of Mathematics ul. Bankowa 14, 40-007 Katowice, Poland, J.Matkowski@wmie.uz.zgora.pl
Bibliografia
- [1] D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.
- [2] A. Bruckner, Minimal superadditive extensions of superadditive functions, Pacific J. Math. 10 (1960), 1155-1162.
- [3] P.R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., Toronto-New York-London, 1950.
- [4] E. Hille, R.S. Phillips, Functional analysis and semigroups, American Mathematical Society Colloquium Publications XXXI, A.M.S., Providence, R.I., 1957.
- [5] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Inequality, Uniwersytet Śląski-PWN, Warszawa-Kraków-Katowice, 1985 (Second edition, Edited with a preface of Attila Gilányi, Birkäuser Verlag, Basel, 2009).
- [6] J. Matkowski, The converse of the Minkowski's inequality theorem and its generalization, Proc. Amer. Math. Soc. 109 (1990), 663-675.
- [7] J. Matkowski, T. Świątkowski, Quasi-monotonicity, Subadditive bijections of R+, and a characterization of Lp-norm, J. Math. Anal. Appl. 154 (1991), 493-506.
- [8] J. Matkowski, T. Świątkowski, On subadditive functions, Proc. Amer. Math. Soc. 119 (1993), 187-197.
- [9] J. Matkowski, Nonlinear contractions in metrically convex space, Publ. Math. Debrecen45 (1994), 103-114.
- [10] D.A. Raikov, On the addition of point-sets in the sense of Schnirelmann, Mat. Sbornik5 (1939) 47, 425-440 [in Russian].
- [11] R.A. Rosenbaum, Subadditive functions, Duke Math. J. 17 (1950), 227-247.
- [12] H. Steinhaus, Sur les distances des points dans les ensembles de mesure positive, Fund. Math. 1 (1920), 93-104.
- [13] T. Takagi, A simple example of the continuous function without derivative, J. Phys.Math. Soc. Japan. 1 (1903), 176-177.
- [14] B.L. van der Waerden, Ein einfaches Beispiel einer nicht differenzierbaren stetigen Funktion, Math. Z. 32 (1930), 474-475.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0003-0029