Ostrowski, Grüss, Cebysev type inequalities for functions whose second derivatives belong to Lp(a, b) and whose modulus of second derivatives are convex

RAFIQ, ARIF; AHMAD, FAROOQ

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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.41 no.1 Bogotá Jan./June 2007

Ostrowski, Grüss, Cebysev type inequalities for functions whose second derivatives belong to L_p(a, b) and whose modulus of second derivatives are convex

Desigualdades del tipo Ostrowski, Grüss, Cebysev para funciones cuya segunda derivada pertenece a L_p(a, b) y cuyo módulo de segunda derivada es convexo

ARIF RAFIQ¹, FAROOQ AHMAD²

¹COMSATS Institute of Information Technology, Department of Mathematics, Technology Plot 30, H-8/1, Islamabad 44000, Pakistaná.
E-mail: arafiq@comsats.edu.pk
²Bahauddin Zakariya University, Centre for Advanced Studies in Pure and Applied Mathematics, Multan 60800, Pakistaná.
E-mail: farooqgujar@gmail.com

Abstract

Ostrowski, Grüss, Cebysev type inequalities involving functions whose second derivatives belong to L_p(a,b) and whose modulus of second derivatives are convex are established. The results provide better bounds than those currently available in the literature.

Key words: Ostrowski Grüss Cebysev inequalities, modulus of second derivative convex, convex function.

2000 Mathematics Subject Classification. Primary: 65C10. Secondary: 65A12.

Resumen

Se establecen desigualdades de tipo Ostrowski, Grüss, Cebysev que comprenden funciones cuyas segundas derivadas pertenecen a L_p(a,b) y cuyos módulos de segundas derivadas son convexos. Los resultados obtenidos proporcionan mejores cotas que las actualmente disponibles en la literatura.

Palabras clave: Inecuaciones de Ostrowski Grüss Cebysev, modulos convexos de segunda derivada, función convexa.

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References

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(Recibido en agosto de 2006. Aceptado en marzo de 2007)