Recently, the authors introduced and studied certain subclasses of analytic functions (associated with the generalized hypergeometric function) using the classical normalization. The main object of this sequel to the earlier work is to present a systematic investigation of various subclasses of analytic functions using Montel's normalization. Coefficients estimates, distortion theorems, and the radii of convexity and starlikeness for each of these classes are given.

Certain Subclasses of Analytic Functions Associated with the Generalized Hypergeometric Function

Univalent functions, fractional calculus, and their applications , edited by H. M. Srivastava and S. Owa. Pp 404. £39·95. 1989. ISBN 0-7458-0701-1 (Ellis Horwood)

http://www.doiserbia.nb.rs/ft.aspx?id=0354-51801305831S

Coefficient estimates for a certain subclass of analytic and bi-univalent functions

: Documentation is given for some subroutines which compute potentials and other functions. A set of subroutines uses rational approximations to compute Bessel functions of integral order. One subroutine uses the Debye approximation for the efficient computation of Bessel functions of complex argument and complex order. Empirical formulae have been developed to express the limiting boundaries of the modes of computation. (Author)

/pdf/computation-of-special-functions-m37di5noj9.pdf

Computation of Special Functions

On univalent functions with negative coefficients

A certain subclass T›(n;p;‚;fi)of starlike functions in the unit disk is introduced. The object of the present paper is to derive several interesting properties of functions belonging to the class T›(n;p;‚;fi): Coe-cient inequalities, distortion the- orems and closure theorems of functions belonging to the class T›(n;p;‚;fi) are determined. Also we obtain radii of convexity for the class T›(n;p;‚;fi): Furthermore, integral operators and modi- fled Hadamard products of several functions belonging to the class T›(n;p;‚;fi) are studied here.

/pdf/on-a-subclass-of-certain-starlike-functions-with-negative-3b5pm2mx1i.pdf

On a subclass of certain starlike functions with negative coefficients

In the present investigation, we consider two new subclasses N Σ (; ) and N Σ ( ; ) of bi- univalent functions defined in the open unit disk U = {z : |z| < 1}: Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.

/pdf/coefficient-bounds-for-new-subclasses-of-bi-univalent-lx4bgzeamn.pdf

Coefficient bounds for new subclasses of bi-univalent functions

The main object of this paper is to give sufficient conditions for certain families of integral operators, which are defined here by means of the normalized form of the generalized Bessel functions, to be univalent in the open unit disk. In particular cases, we find the corresponding simpler conditions for integral operators involving the Bessel function, the modified Bessel function and the spherical Bessel function.

/pdf/some-sufficient-conditions-for-univalence-of-certain-134o4d3l2z.pdf

Some Sufficient Conditions for Univalence of Certain Families of Integral Operators Involving Generalized Bessel Functions

In the present work our object is to establish some geometric properties (like univalence, starlikeness, convexity and close-to-convexity) for the generalized Struve functions. In order to prove our main results, we use the technique of differential subordinations developed by Miller and Mocanu, some inequalities, and some classical results of Ozaki and Fejer.

https://content.sciendo.com/downloadpdf/journals/aicu/ahead-of-print/article-10.2478-aicu-2014-0007.pdf

Geometric Properties of Generalized Struve Functions

We give sufficient conditions for the parameters of the normalized form of the generalized Struve functions to be convex and starlike in the open unit disk.

/pdf/starlikeness-and-convexity-of-generalized-struve-functions-43ibnqs73v.pdf

Halit Orhan

Papers

On a subclass of certain starlike functions with negative coefficients

Coefficient bounds for new subclasses of bi-univalent functions

Some Sufficient Conditions for Univalence of Certain Families of Integral Operators Involving Generalized Bessel Functions

Geometric Properties of Generalized Struve Functions

Starlikeness and Convexity of Generalized Struve Functions