Ostrowski Type Inequalities on Time Scales for Double Integrals

Abstract

In this paper we first derive an Ostrowski type inequality on time scales for double integrals via -integral which unify corresponding continuous and discrete versions. We then replace the -integral by the ∇∇-, ∇-, and ∇ -integrals and get completely analogous results.

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

“…In recent years, various generalizations of the Ostrowski inequality including continuous and discrete versions have been established (for example, see [3][4][5][6][7][8][9][10][11][12][13][14] and the references therein). On the other hand, Hilger [15] initiated the theory of time scales as a theory capable of treating continuous and discrete analysis in a consistent way, based on which some authors have studied the Ostrowski type inequalities on time scales (see [16][17][18][19][20][21][22][23][24]). The established Ostrowski type inequalities on time scales unify continuous and discrete analysis, and can be used to provide explicit error bounds for some known and some new numerical quadrature formulae.…”

Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals

“…Due to the wide application of fractional integrals, some authors extended to study fractional HermiteHadamard, Grüss, or Ostrowski type inequalities for functions of different classes, see [2,11,13,14,15,16,23,26] where further references are listed.…”

Estimates of Certain Integral Inequalities on Time Scales

“…Recently, many authors have studied various aspects of dynamic inequalities on time scales using various techniques [1][2][3][4]. In this paper, we obtain explicit bounds on certain integral inequalities on time scales.…”