On an operatorial inequality

• Autorzy: Popa V. , Lungu N.
• Języki publikacji: EN

Abstrakty

EN

In this paper we give an operatorial inequality which is applied to find estimations for the solutions of some integral and differential systems of inequalities.

Słowa kluczowe

EN

inequality; operators; differential operator

PL

operatory; nierówności; operatory całkowe; operatory różniczkowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 3
• Strony: 667--674
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Popa V.

• Technical University, Department of Mathematics, Str. C. Daicoviciu 15, 3400 Cluj-Napoca, Romania

autor

Lungu N.

• Technical University, Department of Mathematics, Str. C. Daicoviciu 15, 3400 Cluj-Napoca, Romania

Bibliografia

• [1] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, 1991.
• [2] E. Hille, Methods in Classical and Functional Analysis, Reading Mass., 1972.
• [3] N. S. Kurpel, B. A. Shuvar, On operator and integral inequalities, Ukrain. Math. J. 3 (1973), 386-390.
• [4] V. Lakshmikantham, S. Leela and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, New York, 1989.
• [5] L. Losonczi, A generalization of the Gronwall-Belmann lemma in partially ordered Banach spaces, J. Math. Anal. Appl. 31 (1970), 668-681.
• [6] N. Lungu, On some Gronwall-Bihari-Wendorff type inequalities, Seminar on Fixed Point Theory, Cluj-Napoca, 3(2002), 3-12.
• [7] D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, 1991.
• [8] B. G. Pachpatte, Inequalities for Differential and Integral Equations, Academic Press, New York, 1988.
• [9] I. A. Rus, Generalized Contractions and Applications, Cluj University Press, 2001.
• [10] I. A. Rus, Picard operators and applications, Sci. Math. Japon. 1 (2003), 191-219.
• [11] V. Stetsenko, M. Shabaan, On operatorial inequalities analogous to Gronwall-Bihari ones, D.A.N. Tadj 7 (1986), 393-398.
• [12] J. Schroder, Operator Inequalities, Academic Press, New York, 1980.
• [13] J. Szarski, Differential Inequalities, PWN-Polish Scientific Publishers, Warszawa, 1965.
• [14] M. Zima, The abstract Gronwall lemma for some nonlinear operators, Demonstratio Math. 31 (1998), 325-332.