Inclusion and Subordination Properties of Multivalent Analytic Functions Involving Cho-Kwon-Srivastava Operator

- Journal title : Kyungpook mathematical journal
- Volume 55, Issue 4, 2015, pp.1031-1051
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2015.55.4.1031

Title & Authors

Inclusion and Subordination Properties of Multivalent Analytic Functions Involving Cho-Kwon-Srivastava Operator

PATEL, JAGANNATH; SAHOO, ASHOK KUMAR;

PATEL, JAGANNATH; SAHOO, ASHOK KUMAR;

Abstract

The object of the present paper is to derive some inclusion and subordination results for certain classes of multivalent analytic functions in the open unit disk, which are defined in terms of the Cho-Kwon-Srivastava operator. Some interesting corollaries are derived and the relevant connection of the results obtained in this paper with various known results are also pointed out.

Keywords

p-valent function;Subordination;Hadamard product;Linear operator;differintegral operator;

Language

English

References

1.

M. K. Aouf, A. Shamandy, A. O. Mostafa and E. A. Adwan, Differential sandwich theorems for multivalent analytic functions defined by the Srivastava-Attiya operator, Bull. Math. Anal. Appl., 3(3)(2011), 227-238.

2.

B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 159(2004), 737-745.

3.

N. E. Cho, O. S. Kwon and H. M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl., 292(2004), 470-483.

4.

J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of acertain family of integral operators, J. Math. Anal. Appl., 276(2002), 432-445.

5.

B. A. Frasin, Family of analytic functions of complex order, Acta Math. Acad. Paedagog. Nyhazi.(N.S.), 22(2006), 179-191.

6.

R. M. Goel and N. S. Sohi, A new criterion for p-valent functions, Proc. Amer. Math. Soc., 78 (1980), 353-357.

7.

S. P. Goyal, P. Goswami and H. Silverman, Subordination and superordination results for a class of analytic multivalent functions, Internat. J. Math. Math. Sci., Vol. 2008, Art. ID 561638, DOI: 10:1155/2008/561638, 1-12.

8.

H. Imrak and R. K. Raina, The starlikeness and convexity of multivalent functions involving certain inequalities, Rev. Mat. Complut., 16(2)(2003), 391-398.

9.

J.-L. Liu and K. I. Noor, Some properties of Noor integral operator, J. Natur. Math., 21(2002), 81-90.

10.

K. I. Noor, Some classes of p-valent analytic functions defined by certain integral operator, Appl. Math. Comput., 157(2004), 835-840.

11.

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.

12.

K. I. Noor, S. Z. H. Bukhari, M. Arif and M. Nazir, Some properties of p-valent analytic functions involving Cho-Kwon-Srivastava integral operator, J. Classical Anal., 3(1)(2013), 35-43.

13.

S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J., 28(1981), 157-171.

14.

S. S. Miller and P. T. Mocanu, Univalent solutions of Briot-Bouquet differential subordinations, J. Differential Equations, 58(1985), 297-309.

15.

S. S. Miller and P. T. Mocanu, Differential Subordinations:Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York and Basel, 2000.

16.

S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39(5)(1987), 1057-1077.

17.

J. Patel and A. K. Mishra, On certain subclasses of multivalent functions associated with an extended fractional differintegral operator, J. Math. Anal. Appl., 332(1)(2007), 109-122.

18.

J. Patel, N. E. Cho and H. M. Srivastava, Certain subclasses of multivalent functions associated with a family of linear operators, Math. Comput. Modelling, 43(2006), 320-338.

20.

H. Saitoh, A linear operator and its application of first order differential subordinations, Math. Japon., 44(1996), 31-38.

21.

T. N. Shanmugam, S. Sivasubramanian and H. M. Srivastava, Differential sandwich theorems for certain subclasses of analytic functions involing multiplier transformations, Integral Transforms Spec. Funct., 17(12)(2006), 889-899.

22.

H. M. Srivastava and M. K. Aouf, A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients I, J. Math. Anal. Appl., 171(1)(1992), 1-13.

23.

H. M. Srivastava and A. Y. Lashin, Some applications of Briot-Bouquet differential subordination, J. Ineq. Pure Appl. Math., 6(2)(2005), 1-7.

24.

H. M. Srivastava and A. K. Mishra, A fractional differintegral operator and its applications to a nested class of multivalent functions with negative coefficients, Adv. Stud. Contemp. Math. (Kyungshang), 7(2)(2003), 203-214.

25.

D. R. Wilken and J. Feng, A remark on convex and starlike functions, J. London Math. Soc., 21(2)(1980), 287-290.

26.

E. T. Whittaker and G. N.Watson, A Course on Modern Analysis: An Introduction to the General Theory of Infinite Processess and of Analytic Functions: With an Account of the Principal Transcendental Functions, Fourth Edn., Cambridge University Press, 1927 (Reprinted).