For Denjoy–Carleman differential function classes C where the weight sequence M = (Mk) is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is C if it maps C -curves to C -curves. The category of C -mappings is cartesian closed in the sense that C (E, C (F, G)) = C (E × F, G) for convenient vector spaces. Applications t...

In this paper, we study integral inequalities which will provide refinements of bounds unified operators established for convex and α , m -convex functions. A new definition function, namely, strongly id="M3"> function is applied in different forms ...

The main aim of this paper is to give refinement bounds fractional integral operators involving extended generalized Mittag-Leffler functions. A new definition, namely, strongly α , m -convex function introduced obtain improvements fo...

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a linear combination of the basis functions. By assuming that the coefficient matrix admits a sparse low-rank structure, we formulate the function estimation prob...

We extend the notion of minimal volume ellipsoid containing a convex body in $$\mathbb {R}^{d}$$ to setting logarithmically concave functions. consider vast class functions whose superlevel sets are concentric ellipsoids. For fixed function from this class, we set all its “affine” positions. any log-concave f on {R}^{d},$$ belonging positions, and find one with integral under condition that it ...

holds for r > 0 and n∈N. We call the left-hand side of this inequality Alzer’s inequality [1] and the right-hand side Martins’ inequality [8]. Let {ai}i∈N be a positive sequence. If ai+1ai−1 ≥ ai for i ≥ 2, we call {ai}i∈N a logarithmically convex sequence; if ai+1ai−1 ≤ ai for i≥ 2, we call {ai}i∈N a logarithmically concave sequence. In [2], Martins’ inequality was generalized as follows: let ...

in the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.