In this paper we derive weighted Ostrowski, Ostrowski-Grüss and Ostrowski-Čebyšev type inequalities on time scales. We also give some other interesting inequalities on time scales as special cases.

We present some inequalities of Ostrowski and trapezoid type with complex exponential weight, for complex-valued absolutely continuous functions. These inequalities are related to Pompeiu’s mean value theorem. Special cases of these inequalities are applied to obtain (i) some approximation results for the finite Fourier and Laplace transforms; (ii) refinements of the Ostrowski and trapezoid ine...

A main class of inequalities including generalized Ostrowski and Ostrowski-Grüss inequalities is established in ] , [ 1 b a L and ] , [ b a L spaces. As this class can be corresponded to a weighted approximation formula, new inequalities can be obtained by using its upper and lower bounds. Some illustrative examples such as three new generalizations of Ostrowski and Ostrowski-Grüss inequalities...

Aim Our purpose was to write a biography of Stanisław Ostrowski that would address in the first place the medical aspect of his professional life, with a comprehensive approach of others fields of his activity. Methods We essentially grounded the paper on primary resources that were papers authored by Ostrowski including his scientific publications, memories, speeches as well as contemporaneo...

where f : [a, b] → R is a differentiable function such that |f ′ (x) | ≤ M for all x ∈ [a, b] . More about Ostrowski type inequalities and companion inequalities to the Ostrowski type inequality can be found in papers [4, 5] and in monographs [1, 6]. If f is a differentiable function, f ′ is integrable, and γ ≤ f ′ (s) ≤ Γ, for all s ∈ [a, b] , then the following Ostrowski–Grüss inequality can ...

We present an elementary three pass algorithm for computing addition in Ostrowski numerations systems. When a is quadratic, addition in the Ostrowski numeration system based on a is recognizable by a finite automaton. We deduce that a subset of X ⊆Nn is definable in (N,+,Va), where Va is the function that maps a natural number x to the smallest denominator of a convergent of a that appears in t...

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.

be a power series with the radius of convergence 1. We say that it has Ostrowski gaps p if there exists a pi, such that | an \ < pn for mk á « Û «*. It has infinite Ostrowski gaps p (pp there corresponds a pair of infinite sequences mk and nk (depending on p') with mk<nk and lim nk/mk= « such that | a» | ...

Many error inequalities in polynomial interpolation can be found in [1, 7]. These error bounds for interpolating polynomials are usually expressed by means of the norms ‖ · ‖p, 1≤ p ≤∞. Some new error inequalities (for corrected interpolating polynomials) are given in [10, 11]. The last mentioned inequalities are similar to error inequalities obtained in recent years in numerical integration an...

Using a variant of Grüss inequality, to give a new proof of a well known result on Ostrowski-Grüss type inequalities and sharpness of this inequality is obtained. Moreover, a new general sharp Ostrowski-Grüss type inequality is given.