A Class of Inequalities Involving Generalized Ostrowski and Ostrowski-Grüss inequalities and Applications
نویسندگان
چکیده
A main class of inequalities including generalized Ostrowski and Ostrowski-Grüss inequalities is established in ] , [ 1 b a L and ] , [ b a L spaces. As this class can be corresponded to a weighted approximation formula, new inequalities can be obtained by using its upper and lower bounds. Some illustrative examples such as three new generalizations of Ostrowski and Ostrowski-Grüss inequalities are given in this sense. Finally, by using the aforementioned approximation formula, a three point quadrature rule involving several well known quadratures is introduced and its error bounds are obtained.
منابع مشابه
New Jensen and Ostrowski Type Inequalities for General Lebesgue Integral with Applications
Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.
متن کاملSome new Ostrowski type fractional integral inequalities for generalized $(r;g,s,m,varphi)$-preinvex functions via Caputo $k$-fractional derivatives
In the present paper, the notion of generalized $(r;g,s,m,varphi)$-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo $k$-fractional derivatives. At the end, some applications to special means are given.
متن کاملWeighted Ostrowski, Ostrowski-grüss and Ostrowski-čebyšev Type Inequalities on Time Scales
In this paper we derive weighted Ostrowski, Ostrowski-Grüss and Ostrowski-Čebyšev type inequalities on time scales. We also give some other interesting inequalities on time scales as special cases.
متن کاملOstrowski type inequalities for functions whose derivatives are preinvex
In this paper, making use of a new identity, we establish new inequalities of Ostrowski type for the class of preinvex functions and gave some midpoint type inequalities.
متن کاملA New Generalization of Ostrowski-grüss Type Inequalities Involving Functions of Two Independent Variables
The main purpose of this paper is to derive a new inequality of Ostrowski-Grüss type with a parameter involving functions of two independent variables.
متن کامل