In this paper we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number α. We prove that this system has deep connections with the Sturmian graph associated with α. We provide several properties of the representations of the natural integers in this system. In particular, we prove that the set of lazy representations of the natural ...

In this paper‎, ‎making use of a new identity‎, ‎we establish new‎ ‎inequalities of Ostrowski type for the class of preinvex functions and‎ ‎gave some midpoint type inequalities‎.

We consider inequalities which incorporate both Jensen and Ostrowski type inequalities for functions with absolutely continuous n-th derivative. We provide applications of these inequalities for divergence measures. In particular, we obtain inequalities involving higher order χ-divergence.

Some inequalities of Ostrowski type for isotonic linear functionals defined on a linear class of function L := {f : [a, b] → R} are established. Applications for integral and discrete inequalities are also given.

A theorem of A. Ostrowski describing meromorphic functions f such that the family {f(λz) : λ ∈ C∗} is normal, is generalized to holomorphic maps from C∗ to a projective space. MSC 2010: 30D45, 32A19.

An approximation of the Stieltjes integral of bounded integrals and continuous integrators via the Darst-Pollard inequality is given. Applications for the generalised trapezoid formula and the Ostrowski inequality for functions of bounded variation are also provided.

A generalisation of a perturbed version of the Ostrowski inequality for twice differentiable mappings is studied. It is shown that the error bounds are better than those obtained previously. Applications for general quadrature formulae are also given.

Using some techniques developed by Dragomir and Wang in the recent paper [2] in connection to Ostrowski integral inequality, we point out some approximation results for the Henkel’s transform of absolutely continuous mapping.