A generalization of Ostrowski inequality on time scales for k points

In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases.Comment: 10 page

Some new generalized 2D Ostrowski-Grüss type inequalities on time scales

AbstractIn this paper, we present some new generalized 2D Ostrowski-Grüss type integral inequalities on time scales, which on one hand extend some known results in the literature, and on the other hand unify corresponding continuous and discrete analysis. New bounds for the 2D Ostrowski-Grüss type inequalities are derived, some of which are sharp

Generalized double-integral Ostrowski type inequalities on time scales

AbstractAn Ostrowski type inequality for a double integral is derived via a ΔΔ-integral on time scales; this generalizes an Ostrowski type inequality and some related results from Liu et al. (2010) [1]. Some new applications are also given

Probability theory on time scales and applications to finance and inequalities

In this dissertation, the recently discovered concept of time scales is applied to probability theory, thus unifying discrete, continuous and many other cases. A short introduction to the theory of time scales is provided. Following this preliminary overview, the moment generating function is derived using a Laplace transformation on time scales. Various unifications of statements and new theorems in statistics are shown. Next, distributions on time scales are defined and their properties are studied. Most of the derived formulas and statements correspond exactly to those from discrete and continuous calculus and extend the applicability to many other cases. Some theorems differ from the ones found in the literature, but improve and simplify their handling. Finally, applications to finance, economics and inequalities of Ostrowski and Grüss type are presented. Throughout this paper, our results are compared to their well known counterparts in discrete and continuous analysis and many examples are given --Abstract, page iii

Weighted Ostrowski, Trapezoid and Grüss type inequalities on time scales

Abstract. In this paper we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski, trapezoid and Grüss type inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases

Weighted Ostrowski type inequalities via Montgomery identity involving double integrals on time scales

In this paper, the Montgomery identity is generalized for double integrals on time scales by employing a novel analytical approach to develop the generalized Ostrowski type integral inequalities involving double integrals. Some inimitable cases are discussed for different parameters and parametric functions. Moreover, applications to some particular time scales are also presented