Generalizations of Opial-type inequalities in several independent variables

• Autorzy: Andric M. , Barbir A. , Pečarić J. , Roqia G.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider Willett’s and Rozanova’s generalizations of Opial’s inequality and extend them to inequalities in several independent variables. Also, we present some new Opial-type inequalities in several independent variables.

Słowa kluczowe

EN

Opial-type inequalities; Willett inequality; Rozanova’s inequality; several independent variables

PL

nierówność Opiala; nierówność Willetta; nierówność Rozanovej; zmienne niezależne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 4
• Strony: 839--847
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Andric M.

• Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Matice Hrvatske 15, 21000 Split, Croatia

autor

Barbir A.

• Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Matice Hrvatske 15, 21000 Split, Croatia

autor

Pečarić J.

• Faculty of Textile Technology, University of Zagreb, Prilaz Baruna Filipovica 28a, 10000 Zagreb, Croatia

autor

Roqia G.

• Abdus Salam School of Mathematical Sciences, 68-B, New Muslim Town, Lahore 54000, Pakistan

Bibliografia

• [1] R. P. Agarwal, P. Y. H. Pang, Opial Inequalities with Applications in Differential and Difference Equations, Kluwer Academic Publishers, Dordrecht, Boston, London, 1995.
• [2] M. Andric, A. Barbir, J. Pecaric, On Willett’s, Godunova–Levin’s and Rozanova’s Opial type inequalities with related Stolarsky type means, Math. Notes, (2014), to appear.
• [3] I. Brnetic, J. Pecaric, Note on generalization of Godunova–Levin–Opial inequality, Demonstratio Math. 3(30) (1997), 545–549.
• [4] I. Brnetic, J. Pecaric, Note on the generalization of the Godunova–Levin–Opial type inequality in several independent variables, J. Math. Anal. Appl. 215 (1997), 274–283.
• [5] D. S. Mitrinovic, J. Pecaric, A. M. Fink, Inequalities Involving Functions and their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1991.
• [6] Z. Opial, Sur une inégalité, Ann. Polon. Math. 8 (1960), 29–32.
• [7] J. E. Pecaric, F. Proschan, Y. C. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Inc., 1992.
• [8] G. I. Rozanova, Integral inequalities with derivatives and with arbitrary convex functions, Uc. Zap. Mosk. Gos. Ped. In-ta im. Lenina 460 (1972), 58–65.
• [9] D. Willett, The existence–uniqueness theorem for an n-th order linear ordinary differential equation, Amer. Math. Monthly 75 (1968), 174–178.