Some new generalizations of Maroni inequality on time scales

• Autorzy: Yin L. , Zhao C.
• 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

EN

Opial inequality; Maroni inequality; Hölder inequality; time scales; delta differentiability

PL

nierówność Opiala; nierówność Maroni; nierówność Höldera; skala czasowa

• 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

autor

Zhao C.

• Department of Mathematics, China Jiliang University, Hangzhou, 310000, P.R. China

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.