Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables

Abstract

In this article, we establish some new Ostrowski type integral inequalities on time scales involving functions of two independent variables for k 2 points, which on one hand unify continuous and discrete analysis, on the other hand extend some known results in the literature. The established results can be used in the estimate of error bounds for some numerical integration formulae, and some of the results are sharp.

Generalized Weighted Ostrowski, Trapezoid and Grüss Type Inequalities on Time Scales

“…Some various generalizations and extensions of the dynamic Ostrowski inequality can be found in the papers [34,33,5,18,50,24,32,37,45,47,48,43,42,41].…”

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

“…Our first result will extend Theorem 10 to the 2-dimensional case (see Remark 15). As a special case (for λ = 0) of our results, we will obtain the main theorems of Feng and Meng in [7] (see Remarks 15,17 and 20); and for λ ∈ (0, 1], we obtain completely new results in this direction.…”

“…In 2012, Feng and Meng [7] extended, among other things, Theorem 9 to the 2-dimensional case. For more on this and related results in this direction, see the papers [9,10,[12][13][14]16] and the references therein.…”

Kamenev Type Oscillatory Criteria for Linear Conformable Fractional Differential Equations

“…There are a lot of papers involving the oscillation for (2) and other linear, nonlinear, damped, and forced differential equations or Hamiltonian systems (see [8][9][10][11]) since the foundation work of Wintner [11] (see also for [12][13][14][15][16][17][18][19][20][21][22][23][24][25]). Especially, if ( ) ≡ 1, we obtain the second-order linear Hill equation ( ) + ( ) ( ) = 0.…”