Suficient condition for q-starlike and q-convex functions associated with generalized confluent hypergeometric function

Öz

The main object of this paper is to investigate and determine a sufficient condition for q-starlike and q-convex functions which are associated with generalized confluent hypergeometric function. The main object of this paper is to investigate and determine a sufficient condition for q-starlike and q-convex functions which are associated with generalized confluent hypergeometric function.The main object of this paper is to investigate and determine a sufficient condition for q-starlike and q-convex functions which are associated with generalized confluent hypergeometric function.

Anahtar Kelimeler

• Univalent functions
• convex and q-convex functions
• starlike and q-starlike functions
• q-derivative operator
• q-number
• generalized confluent hypergeometric function

Kaynakça

1. [1] Agrawal S. and Sahoo S. K., A generalization of starlike functions of order. Hokkaido Math. J., 46(1) (2017), 15-27.
2. [2] Duren P. L., Univalent Functions. Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
3. [3] Hille E., Hypergeometric functions and conformal mappings. J. Differential Equations, 34 (1979) 147–152.
4. [4] Ismail M. E. H., Merkes E. and Styer D., A generalization of starlike functions. Complex Variables Theory Appl., 14 (1990), 77-84.
5. [5] Janowski W., Some extremal problems for certain families of analytic functions. Ann. Polon. Math., 28 (1973), 297-326.
6. [6] Lehto O., and Virtanen K. I., Quasiconformal mappings in the plane (Grundlehren Math. Wiss. vol. 126), 2nd ed., Springer, Berlin, 1973.
7. [7] Owa S. and Srivastava H. M. (Eds.), Current Topics in Analytic Function Theory. World Scientific Publishing Company, Singapore, New Jersey, London, Hong Kong, 1992. [8] Ponnusamy S., Close-to-convexity properties of Gaussian hypergeometric functions. J. Comput. Appl. Math., 88 (1997), 327-337. [9] Ponnusamy S. and Ronning F., Starlikeness properties for convolutions involving hypergeometric series, Ann. Univ. Mariae Curie-Sk lodowska Sect., L.II. 1 (16) (1998), 141–155.