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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-7ed5a2bf-8721-47f2-b27d-461aa064279c

Czasopismo

Demonstratio Mathematica

Tytuł artykułu

Some new generalizations of Maroni inequality on time scales

Autorzy Yin, L.  Zhao, C. 
Treść / Zawartość http://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
EN The aim of present paper is to establish some new integral inequalities on time scales involving several functions and their derivatives which in the special cases yield the well known Maroni inequality and some of its generalizations.
Słowa kluczowe
PL nierówność Opiala   nierówność Maroni   nierówność Höldera   skala czasowa  
EN Opial inequality   Maroni inequality   Hölder inequality   time scales   delta differentiability  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2013
Tom Vol. 46, nr 4
Strony 645--654
Opis fizyczny Bibliogr. 16 poz.
Twórcy
autor Yin, L.
  • Department of Mathematics and Information Science, Binzhou University, Binzhou City, Shandong Province, 256603, China, yinli_79@163.com
autor Zhao, C.
  • Department of Mathematics, China Jiliang University, Hangzhou, 310000, P.R. China, chjzhao@163.com
Bibliografia
[1] R. P. Agarwal, P. Y. H. Pang, Opial Inequalities with Applications in Differential and Difference Equations, Kluwer, Dordreht., 1995.
[2] D. W. Boyd, J. S. W. Wong, An extension of Opial’s inequality, J. Math. Anal. Appl. 190(2) (1995), 559–577.
[3] K. M. Das, An inequality similar to Opial’s inequality, Proc. Amer. Math. Anal. Soc. 22 (1969), 258–261.
[4] L. K. Hua, On an inequality of Opial, Sci. China Ser. A 14 (1965), 789–790.
[5] A. Lasota, A discrete boundary value problem, Ann. Polon. Math. 20 (1968), 183–190.
[6] J. D. Li, Opial-type integral inequalities involving several higher order derivatives, J. Math. Anal. Appl. 167(1) (1992), 98–110.
[7] D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, New York, 1970.
[8] B. G. Pachpatte, On Opial-type integral inequalities, J. Math. Anal. Appl. 120(2) (1986), 547–556.
[9] B. G. Pachpatte, A note on Opial and Wirtinger type discrete inequalities, J. Math. Anal. Appl. 127(2) (1987), 470–474.
[10] P. Maroni, Sur l’inégalitéd’Opial-Beesack, C. R. Math. Acad. Sci. Paris 264 (1967), A62–A64.
[11] B. G. Pachpatte, On Opial-type discrete inequalities, An. Stiint. Univ. Al. I. CuzaIasi. Mat. (N.S.) 36 (1990), 237–240.
[12] R. Agarwal, M. Bohner, A. Peterson, Inequalities on time scales: a survey, Math. Inequal. Appl. 4 (2001), 537–557.
[13] B. Kappuz, U. Özkan, Some generalizations for Opial’s inequality involving several functions and their derivatives of arbitrary order on arbitrary time scales, Math. Inequal. Appl. 14(1) (2011), 79–92.
[14] H. M. Srivastava, K. L. Tseng, S. J. Tseng, J. C. Lo., Some generalizations of Maroni’s inequality on time scales, Math. Inequal. Appl. 14(2) (2011), 469–480.
[15] B. G. Pachpatte, On certain integral inequalities related to Opial’s inequality, Period. Math. Hungar. 17(2) (1986), 119–125.
[16] P. R. Beesack, On an integral inequalities of Z. Opial, Trans. Amer. Math. Soc. 104 (1962), 470–475.
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