Explicit bounds on some retarded integral inequalities

• Autorzy: Pachpatte B. G.
• Języki publikacji: EN

Abstrakty

EN

In this paper we establish some new retarded integral inequalities which provide explicit bounds on unknown functions. Applications are also given to illustrate the usefulness of one of our results.

Słowa kluczowe

EN

explicit bound; retarded integral inequalities; partial derivatives; nondecreasing; estimate on the solution; uniueness of solution; dependency of solution

PL

nierówność całkowa

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2005
• Tom: Nr 35
• Strony: 85--98
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Pachpatte B. G.

• 57 Shri Niketan Colony, Near Abhinay Talkies, Aurangabad 431 001 (Maharashtra) India,

Bibliografia

• [1] D. Bainov, p. Simeonov, Integral Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1992.
• [2] L.E. El'sgol'ts, S.B. Norkin, Introduction to the theory and applications of differential equations with deviating arguments, Academic Press, New York, 1973.
• [3] O. Lipovan, a retarded Gronwall-like inequality and its applications, J. Math. Anal. Appl., 252(2000), 389-401.
• [4] B.G. Pachpatte, Inequalities for Differential and Integral Equations, Academic Press, New York, 1998.
• [5] B.G. Pachpatte, On some fundamental integral inequalities and their discrete analogues, J. Inequal. Pure and AppL Math., 2(2)Art.15, 2001.
• [6] B.G. Pachpatte, On some retarded integral inequalities and applications, J. Inequal. Pure and Appl. Math., 3(2) Art. 18, 2002.
• [7] B.G. Pachpatte, Explicit bounds on certain integral inequalities, J. Math. Anal. Appl., 267(2002), 48-61.
• [8] W. Walter, Differential and Integral Inequalities, Springer-Verlag, New York, 1970.