For certain dual integral equations involving trigonometric functions and the Bessel function of zeroth order as their kernels solution methods are described. These methods exploit the fact that, under certain circumstances of practical importance, one of the integrals of each set of the dual integral equations under consideration possesses a asquare-rooto singularity at the aturning pointo, i....

We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász extension of a pseudo-Boolean function which vanishes at the origin. We present axiomatizations of this generalized Choquet integral, given in terms of certain functional equations, as well as by necessary and sufficient conditions which reveal desirable propertie...

In this paper we consider the classes of starlike functions of order α, convex functions of order α and we study the convexity and α-order convexity for some general integral operators. Several corollaries of the main results are also considered.

For analytic and multivalent functions f (z) and p(z) in the open unit disk U, a subordi-nation theorem due to Littlewood (1925) which was called the integral mean is applied. Some simple examples for our results are also considered.

Abstract. Recently Breaz and Breaz [4] and Breaz et.al[5] introduced two general integral operators Fn and Fα1,...,αn . Considering the classes N(γ), MT(μ, β) and KD(μ, β) we derived some properties for Fn and Fα1,...,αn . Two new subclasses KDFn(μ, β, α1, ..., αn) and KDFα1,...,αn(μ, β, α1, ..., αn) are defined. Necessary and sufficient conditions for a family of functions fj to be in the KDFn...