New properties of the generalized Dini function

Abstract

In this work we study some properties of the normalized form of generalized Dini function like close-to-convexity of some order and close-to-convex with respect to another convex function. Furthermore, we investigate sufficient conditions which these functions are uniformly $k$-starlike functions of complex order $b$ in the open unit disk, and some consequences of the main results are also presented.

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Keywords

• Analytic functions
• univalent function
• Bessel functions of first kind of order $\nu$
• modified Dini function
• starlike
• convex and close-to-convex functions of order $\alpha$

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