Document Type: Research Paper

Authors

1 Department of Mathematics, Walchand College of Engineering, Sangli 416415, India.

2 Department of Mathematics, Sveri's College of Engineering, Pandharpur 413304, India.

3 Faculty of Mathematics and Computer Science, Babec{s}-Bolyai University, 400084 Cluj-Napoca, Romania.

Abstract

In the present paper, we have established sufficient conditions for Gaus\-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $\mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

Keywords

Main Subjects

[1] M.K. Aouf, A.O. Mostafa, and H.M. Zayed, Some constraints of hypergeometric functions belong to certain subclasses of analytic functions, J. Egyptian Math. Soc., 24 (2016), pp. 1-6.

[2] B.C. Carlson and D.B. Shaffer, Starlike and prestarlike hypergeometric functions, J. Math. Anal. Appl., 15 (1984), pp. 737-745.

[3] P.L. Duren, Univalent functions, Springer-Verlag, New York, 1983.

[4] J. Dziok and H.M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14 (2003), pp. 7-18.

[5] J. Dziok and H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, App. Math. Comput., 103 (1999), pp. 1-13.

[6] Y.E. Hohlov, Operators and operations in the class of univalent functions, Izv. Vyss. Ucebn. Zaved. Mat. (in Russian), 10 (1978) 83-89.

[7] S.S. Joshi, A certain subclass of analytic functions associated with fractional derivative operator, Tamsui Oxf. J. Inf. Math. Sci., 24 (2008), pp. 201-214.

[8] S. Kanas and H.M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transforms Spec. Funct., 9 (2000), pp. 121-132.

[9] J.A. Kim and K.H. Shon, Certain properties for convolutions involving hypergeometric functions, Int. J. Math. Math. Sci., 17 (2003), pp. 1083-1091.

[10] S.R. Kulkarni, Some problems connected with univalent functions, Ph.D. Thesis. Shivaji University, Kolhapur, 1981.

[11] E. Merkes and B.T. Scott, Starlike hypergeometric functions, Proc. Amer. Math. Soc., 12 (1961), pp. 885-888.

[12] M.S. Robertson, On the theory of univalent functions, Ann. Math., 37 (1936), pp. 374-408.

[13] S. Ruscheweyh and V. Singh, On the order of starlikeness of hypergeometric functions, J. Math. Anal. Appl., 113 (1986), pp. 1-11.

[14] N. Shukla and P. Shukla, Mapping properties of analytic function defined by hypergeometric functions, Soochow J. Math., 25 (1999), pp. 19-36.

[15] H. Silverman, Starlike and convexity properties for hypergeometric functions, J. Math. Anal. Appl., 172 (1993), pp. 574-581.

[16] H.M. Srivastava, Some fox-wright generalized hypergeometric functions and associated families of convolution operators, Appl. Anal. Discrete Math., 1 (2007), pp. 56-71.

[17] H.M. Srivastava and S. Owa (eds.), Current topics in analytic function theory, World Sci. Publ., 1992.

[18] H. Tang and G.T. Deng, Subordination and superordination preserving properties for a family of integral operators involving the noor integral operator, J. Egyptian Math. Soc., 22 (2014), pp. 352-361.