Abstract. In this paper a necessary and sufficient condition is deduced for the close-to-convexity of a cross-product of Bessel and modified Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives, the newly discovered power series and infinite product representation of this crossproduct, as well as a slightly modified version of a result of Lorch on the monotonicity of the zeros of the cross-product with respect to the order.Mathematics subject classification (2010): 33C10, 30C45. Keywords and phrases: Bessel functions of the first kind, modified Bessel functions of the first kind, close-to-convex functions, starlike functions, transcendental entire functions, zeros of cross-product of Bessel functions, infinite product.
In this paper a necessary and sufficient condition is deduced for the close-to-convexity of a cross product of Bessel and modified Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives, the newly discovered power series and infinite product representation of this cross-product, as well as a slightly modified version of a result of Lorch on the monotonicity of the zeros of the cross product with respect to the order.
The object of the present paper is to derive distortion inequalities for fractional integral operator of functions in the class $K (n , \alpha, \beta)$ consisting of analytic and univalent functions with negative coefficients.
In terms of linear operators we introduce new classes of functions. Then by using differential subordinations, certain results concerning inclusion relations, coefficient bounds and other results are given.
Abstract. Let A(p) be the class of functions f :n+p−1 (z) by using convolution * as fn+p−1 * fanalytic in E with p(0) = 1, is in the class P k (ρ) if n+p−1 * f for f (z) belonging to this class. We derive some interesting properties of this generalized integral operator which include inclusion results and radius problems.
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