On Grüss, Ostrowski and trapezoid-type inequalities via nabla integral on time scales

Abstract

Ostrowski inequality gives the absolute deviation of the function from its integral mean. Delta and nabla calculi are first two approaches to study time scales calculus. This article presents the Ostrowski inequality for univariate first order nabla differentiable function by using Montgomery identity established for nabla integrals. Some extensions of dynamic Ostrowski-type inequality are investigated with the help of integration by parts for nabla integrals, properties of the modulus and polynomials on time scales. Furthermore, dynamic Grüss and trapezoid-type inequalities are established in their generalized form for twice nabla differentiable functions by utilizing the Montgomery identity. In addition, the obtained inequalities are discussed for continuous and discrete time scales.