Shigeyoshi Owa

Current topics in analytic function theory

Univalent logharmonic extensions onto the unit disk or onto an annulus, Z. Abdulhadi and W. Hengartner hypergeometric functions and elliptic integrals, G.D. Anderson et al a certain class of caratheodory functions defined by conditions on the circle, J. Fuka and Z.J. Jakubowski recent advances in the theory of zero sets of the Bergman spaces, E.A. LeBlanc a coefficient functional for meromorphic univalent functions, L. Liu spherical linear invariance and uniform local spherical convexity, W. Ma and D. Minda a special differential subordination and its application to univalency conditions, S.S. Miller and P.T. Mocanu on the Bernardi integral functions, S. Owa analytic solutions of a class of Briot-Bouquet differential equations, S. Owa and H.M. Srivastava a certain class of generalized hypergeometric functions associated with the Hardy space of analytic functions, H.M. Srivastava on the coefficients of the univalent functions of the Nevanlinna classes N1 and N2, P.G. Todorov.

A class of distortion theorems involving certain operators of fractional calculus

Abstract The object of the present paper is to investigate a general class of fractional integral operators involving the Gauss hypergeometric function. Several interesting distortion theorems for various subclasses of analytic and univalent functions are proved in terms of these operators of fractional calculus. Some special cases of the results presented here are also indicated.

Neighborhoods of certain analytic functions with negative coefficients

The object of the present paper is to derive some properties of neighborhoods of analytic functions with negative coefficients in the open unit disk.

Some fractional differintegral equations

Recently, Nishimoto [J. College. Engrg. Nihon Univ. Ser. B 24 (1983), 7–13] studied a certain fractional integral equation and a system of simultaneous differintegral equations, each of order 12. Motivated by Nishimotos work, Owa and Nishimoto [J. College Engrg. Nihon Univ. Ser. B 24 (1983), 67–72] considered a general fractional differintegral equation. The object of the present paper is to investigate some interesting properties of functions which satisfy the general fractional differintegral equation solved by Owa and Nishimoto.

Close-to-convexity, starlikeness, and convexity of certain analytic functions☆

The main object of the present paper is to derive several sufficient conditions for close-to-convexity, starlikeness, and convexity of certain (normalized) analytic functions. Relevant connections of some of the results obtained in this paper with those in earlier works are also provided.

On certain properties for some classes of starlike functions

Abstract Let f(z) = z + a2z2 + … be analytic in the unit disk U = {z:|z|⩽1}. By using the method of differential subordinations we give a criterion for a function f(z) to be in a certain class L ∗ [a,b] of starlike functions. For functions f(z)∈L ∗ [a,b] a subordination relation for (f(z) z) μ is also given.

Some characterization theorems for starlike and convex functions involving a certain fractional integral operator

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On new classes of analytic functions with negative coefficients.

We introduce the classes Kn* of analytic functions with negative coefficients by using the nth order Ruscheweyh derivative. The object of the present paper is to show coefficient inequalities and some closure theorems for functions f(z) in Kn*. Further we consider the modified Hadamard product of functions fi(z) in Kni*(n=1,2,…,m).

A class of integral operators preserving subordination and superordination for meromorphic functions

The purpose of the present paper is to investigate several subordination- and superordination-preserving properties of a certain class of integral operators, which are defined on the space of meromorphic functions in the punctured open unit disk. The sandwich-type theorem for these integral operators is also presented. Moreover, we consider an application of the subordination and superordination theorem to the Gauss hypergeometric function.

Coefficient bounds for some families of starlike and convex functions of complex order

Abstract In the present work, the authors determine coefficient bounds for functions in certain subclasses of starlike and convex functions of complex order, which are introduced here by means of a family of nonhomogeneous Cauchy–Euler differential equations. Several corollaries and consequences of the main results are also considered.