Megumi Saigo

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Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex(More)
Integral transforms (Hf)(x) = ∞ 0 H m,n p,q xt f (t)dt involving Fox's H-functions as kernels are studied in the spaces L ν,r of functions f such that ∞ 0 |t ν f (t)| r dt t < ∞ (1 ≦ r < ∞, ν ∈ R). Mapping properties such as the boundedness, the representation and the range of the transforms H are given.
Evaluation of integrals Meijer G-function Bessel functions Cosine and sine functions a b s t r a c t This paper is devoted to the study of the special function Z ν ρ (z) of z ∈ C with two parameters ρ ∈ R and ν ∈ C. In a special case such a function coincides with the McDonald function. Using the representations of Z ν ρ (z) in terms of the H-function,(More)
The paper is devoted to study the H-function defined by the Mellin-Barnes integral H p,q (z) = 1 2πi ∫ L H m,n p,q (s)z ds, where the function H p,q (s) is a certain ratio of products of Gamma functions with the argument s and the contour L is specially chosen. The conditions for the existence of Hm,n p,q (z) are discussed and explicit power and(More)
where the function m,n tp,q (S) is a certain ratio of products of the Gammafunctions with the argument s and the contour specially chosen. The conditions for the existence of m,n Hp, q (Z) are discussed and explicit power and power-logarithmic series expansions of m,n Hp, q (Z) near zero and infinity are given. The obtained results define more precisely the(More)