Some New Discrete Inequalities of Opial and Lasota's Type

Hsu Kai-Chen Department of Applied Mathematics, Aletheia University Tamsui, New Taipei City 25103, Taiwan
Kuei-Lin Tseng Department of Applied Mathematics, Aletheia University Tamsui, New Taipei City 25103, Taiwan

Keywords: Holder's inequality, Opial inequality, Lasota inequality, Forward difference operator, Backward difference operator.

In this paper, we establish some new discrete inequalities of Opial and Lasota's type which reduce to some inequalities in [4].

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R. P. Agarwal and P. Y. H. Pang, Opial inequalities with application in differential and difference equations, Kluwer Academic Publishers (1995).

D. Bainov and P. Simeonov, Integral Inequalities and Applications, Kluwer Academic Publishers (1992).

L.-K. Hua, On an inequality of Opail, Scientia Sinica 14 (1965), 789-790.

A. Lasota, A discrete boundary value problem, Ann. Polon. Math. 20 (1968), 183-190.

J. Myjak, Boundary value problems for nonlinear differential and difference equations of the

second order, Zeszyty Nauk. Univ. Jagiellonsi, Prace Math. 15 (1971), 113-123

C. Olech, A simple proof of a certain result of Z. Opial, Ann. Polon. Math. 8 (1960), 61-63.

Z. Opial, Sur une inegalite, Ann. Polon. Math. 8 (1960), 29-32.

B. G. Pachpatte, On Opial like discrete inequalities, An. Sti. Univ. A1. I. Cuza Iasi, Mat. 36

(1990), 237-240.

B. G. Pachpatte, A Note on Opial Type Finite Difference Inequalities, Tamsui Oxford J. Math. Sci. 21(1) (2005), 33-39.

J. S. W. Wong, A discrete analogue of Opial?s inequality, Canadian Math. Bull. 10 (1967), 115-118.

G.-S. Yang, On a certain result of Z. Opial, Proc. Japan Acad. 42 (1966), 78-83.