# Applications of convolution and‎ ‎subordination to certain $p$-valent functions

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎COMSATS Institute of‎ ‎Information Technology Abbotabad‎, ‎Pakistan.

2 Department of Mathematics‎, ‎Institute of‎ ‎Mathematics‎, ‎University of Rzeszow‎, ‎ul‎. ‎Rejtana 16A‎, ‎35-310 Rzeszow‎, ‎Poland.

4 School of Mathematical Sciences‎, ‎Faculty of Science and‎ ‎Technology‎, ‎Universiti Kebangsaan Malaysia‎, ‎Bangi 43600‎, ‎Selangor‎, ‎Malaysia.

5 Department of Mathematics and Statistics‎, ‎International Islamic University Islamabad‎, ‎Pakistan.

Abstract

In this paper we considered some new classes of multivalent functions by using Aouf-Silverman-Srivastava operator and derived some important results using convolution and subordination technique. This new class is an extension of a class which introduced before.

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Main Subjects

### References

M.K. Aouf and J. Dziok, Certain class of analytic functions associated with the Wright generalized hypergeometric functions, J. Math. Appl. 30 (2008) 23--32.

M.K. Aouf, A. Shamandy, A.O. Mostafa and S.M. Madian, Certain class of p-valent functions associated with the Wright generalized hypergeometric, Demonstr. Math. 43 (2010) 39--54.

S.D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969) 429--446.

N.E. Cho, The Noor integral operator and strongly close-to-convex functions, J. Math. Anal. Appl. 238 (2003) 202--212.

J. Dziok and R.K. Raina, Families of analytic functions associated with the Wright generalized hypergeometric functions, Demonstr. Math. 37 (2004) 533--542.

J. Dziok, R.K. Raina and H.M. Srivastava, Some classes of analytic functions associated with operators on Hilbert space involving Wright generalized hypergeometric functions, Proc. Jangieon Math. Soc. 7 (2004) 43--55.

J. Dziok and H.M. Srivastava, Classes of analytic functions associated with the Wright generalized hypergeometric functions, Appl. Math. Comput. 103 (1999) 1--13.

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

D.I. Hallenbeck and S. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc. 52 (1975) 191--195.

S. Hussain and J. Sokół, On a class of analytic functions related to conic domains and associated with Carlson-Shaffer operator, Acta. Math. Sci. 32 (2012), no. 4, 1399--1407.

S. Kanas and A. Wiśniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105 (1999) 327-336.

S. Kanas and A. Wiśniowska, Conic domains and k-starlike functions, Rev. Roumaine Math. Pures Appl. 45 (2000) 647--657.

Y.C. Kim and H.M. Srivastava, Fractional integral and other linear operators associated with the Gaussian hypergeometric function, Complex Variables Theory Appl. 34 (1997) 293--312.

R.J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965) 755--758.

W. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis (Tianjin, 1992), pp. 514--520, Conf. Proc. Lecture Notes Anal. I, Int. Press, Cambridge, MA, 1994.

K.I. Noor, On new classes of integral operators, J. Nat. Geom. 16 (1999) 71--80.

K.I. Noor and M.A. Noor, On integral operators, J. Math. Anal. Appl. 238 (1999) 341--352.

K.I. Noor and M.A. Noor, On certain classes of analytic functions defined by Noor integral operator, J. Math. Anal. Appl. 281 (2003) 244--252.

S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975) 109--115.

J. Sokół, Classes of multivalent functions assoicated with a convolution operator, Appl. Math. Comput. 60 (2010) 1343--1350.

E.M. Wright, The asymptotic expansion of generalized hypergeometric function, Proc. Lond. Math. Soc. (2) 46 (1940) 389--408.

### History

• Receive Date: 29 March 2016
• Revise Date: 05 October 2016
• Accept Date: 09 October 2016