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Generalized multivariate Fink-type identity and some related results on time scales with applications

Hussain Sabir, Latif Muhammad

Journal of Applied Analysis

2019

Vol. 25, nr 2

189--203

Generalized Fink-type identity for multi-variables to an arbitrary time scales is obtained, giving some multi-variate Ostrowski, Iyengar and Grüss-type inequalities unifying the corresponding continuous and discrete version. Some new applications to generalized polynomials are also obtained.

Generalized weighted Ostrowski, Trapezoid and Grüss type inequalities on time scales

El-Deeb A. A., Elsennary H. A., Nwaeze E. R.

Fasciculi Mathematici

2018

Nr 60

123--144

In this article, using two parameters, we obtain generalizations of a weighted Ostrowski type inequality and its companion inequalities on an arbitrary time scale for functions whose first delta derivatives are bounded. Our work unifies the continuous and discrete versions and can also be applied to the quantum calculus case.

A Grüss type inequality for isotonic linear functionals and applications

Dragomir S. S.

Demonstratio Mathematica

2003

Vol. 36, nr 3

551--562

An inequality for a normalised isotonic linear functional of Grüss type and particular cases for integrals and norms are established. Applications in obtaining a counterpart for the Cauchy-Buniakowski-Schwartz inequality for functionals and Jessen's inequality for convex functions are also given.