In this paper, by introducing a technique of parameter functions, we establish a new Ostrowski type inequality on time scales and unify corresponding continuous and discrete versions. Furthermore, some particular integral inequalities on time scales are given as special cases. Mathematics subject classification (2010): 54C30, 26D10, 26D15.

Integral inequalities of Ostrowski type are developed for n−times differentiable mappings, with multiple branches, on the L∞ norm. Some particular inequalities are also investigated, which include explicit bounds for perturbed trapezoid, midpoint, Simpson’s, NewtonCotes and left and right rectangle rules. The results obtained provide sharper bounds than those obtained by Dragomir [5] and Cerone...

We give axiomatizations and quantifier eliminations for first-order theories of finitely ramified valued fields with an automorphism having a close interaction with the valuation. We achieve an analogue of the classical Ostrowski theory of pseudoconvergence. In the outstanding case of Witt vectors with their Frobenius map, we use the ∂-ring formalism from Joyal.

Integral operators with the Mittag–Leffler function in kernels play a very vital role generalizing classical integral inequalities. This paper aims to derive Ostrowski-type inequalities for k-fractional integrals containing functions. Several new can be deduced various fractional particular cases. Applications of these are also given.

The main objective of this paper is to derive some new generalizations Ostrowski type inequalities for the functions whose first derivatives absolute value are harmonically convex. We also discuss special cases obtained results. In last section, we present applications

With his 1979 article "Do we really ever get out of anarchy?" Alfred Cuzán provides us with a wonderful insight: "Anarchy, like matter, never disappears it only changes form." Cuzán argues that anarchy, defined as the absence of a third party territorial monopolist of ultimate jurisdiction, is omnipresent: Regardless of what political system we live under, there will always be anarchic relation...

Some new inequalities of Ostowski-type for the Čebyšev functional and applications for Taylor’s expansion and generalised trapezoid formula are pointed out. Mathematics subject classification (2010): Primary 26D15; Secondary 41A55.

* Correspondence: [email protected] School of Science, Shandong University of Technology, Zhangzhou Road 12, Zibo, Shandong, 255049, China Full list of author information is available at the end of the article Abstract In this article, we establish some new Ostrowski type integral inequalities on time scales involving functions of two independent variables for k points, which on one hand unify con...

It is clear that 0∈ h(Δ). Moreover, (i) if 0 ∈ h(Δ), then h is called spirallike (resp., starlike) with respect to an interior point; (ii) if 0 ∈ h(Δ), then h is called spirallike (resp., starlike) with respect to a boundary point. In this case, there is a boundary point (say, z = 1) such that h(1) := ∠ limz→1h(z)= 0 (see, e.g., [1, 6]); by symbol∠ lim, we denote the angular (nontangential) lim...

An Ostrowski type inequality for general convex functions defined on linear spaces is generalised. Some inequalities which improve the HermiteHadamard type inequality for convex functions defined on linear spaces are derived using the obtained result. The results in normed linear spaces are used to obtain some inequalities which are related to the given norm and associated semi-inner products, ...