In this article, a general integral identity for twice differentiable mapping involving fractional integral operators is derived. As a second, by using this identity we obtained some new generalized Hermite-Hadamards type inequalities for functions whose absolute values of second derivatives are s-convex and concave. The main results generalize the existing Hermite-Hadamard type inequalities in...

In this paper, a class of non-autonomous neural networks with delays is considered. By using the properties of spectral radius of nonnegative matrix, two new integral inequalities are established. Based on the integral inequalities, some new sufficient conditions for the existence of quasi-invariant and attracting sets of the non-autonomous neural networks with delays are obtained. The framewor...

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal...

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 (...

Using Sălăgean differential operator, we study new subclasses of analytic functions. Coefficient inequalities and distortion theorems and extreme points of these classes are studied. Furthermore, integral means inequalities are obtained for the fractional derivatives of these classes.

Some inequalities in 2-inner product spaces generalizing Bessel’s result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.

New inequalities concerning functions of the form f (xy) similar to Hardy-Hilbert’s integral inequality are presented. A new class of functions denoted by (p, q)−-Hö(I) is defined. Many other new inequalities are also given.

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.

Keywords: Fuzzy measure Sugeno integral Choquet integral Stolarsky's inequality a b s t r a c t Recently Flores-Franulič, Román-Flores and Chalco-Cano proved the Stolarsky type inequality for Sugeno integral with respect to the Lebesgue measure k. The present paper is devoted to generalize this result by relaxing some of its requirements. Moreover, Stolar-sky inequality for Choquet integral is ...