tailieunhanh - Radii of uniform convexity of some special functions

In this investigation our main aim is to determine the radii of uniform convexity of selected normalized q -Bessel and Wright functions. Here we consider six different normalized forms of q -Bessel functions and we apply three different kinds of the normalization of the Wright function. | Turk J Math (2018) 42: 3010 – 3024 © TÜBİTAK doi: Turkish Journal of Mathematics Research Article Radii of uniform convexity of some special functions 1 İbrahim AKTAŞ1∗,, Evrim TOKLU2 ,, Halit ORHAN3 , Department of Mathematical Engineering, Faculty of Engineering and Natural Sciences, Gümüşhane University, Gümüşhane, Turkey 2 Department of Mathematics, Faculty of Education, Ağrı İbrahim Çeçen University, Ağrı, Turkey 3 Department of Mathematics, Faculty of Science, Atatürk University, Erzurum, Turkey Received: • Accepted/Published Online: • Final Version: Abstract: In this investigation our main aim is to determine the radii of uniform convexity of selected normalized q -Bessel and Wright functions. Here we consider six different normalized forms of q -Bessel functions and we apply three different kinds of the normalization of the Wright function. We also show that the obtained radii are the smallest positive roots of some functional equations. Key words: Radius of uniform convexity, Mittag-Leffler expansions, q-Bessel functions, Wright function 1. Introduction and preliminaries Special and geometric function theories are the most important branches of mathematical analysis. There has been a close relationship between special and geometric function theories since hypergeometric functions were used in the proof of the famous Bieberbach conjecture. Therefore, most mathematicians have considered some of the geometric properties of special functions that can be expressed by the hypergeometric series. Some of the geometric properties of the Bessel, Struve, Lommel, Wright, and q -Bessel functions in particular have been investigated by many authors. The first important results concerning the geometric properties of hypergeometric and related functions can be found in [14, 22, 23, 29]. In fact, there are some relationships between the geometric properties and the zeros of