A class of multivalent functions defined by generalized Ruscheweyh derivatives involving a general fractional derivative operator
DOI:
https://doi.org/10.4067/S0716-09172014000200005Keywords:
Starlike function, p-valent function, convolution, generalized fractional derivative operator, generalized Ruscheweyh derivatives, función tipo estrella, función p-valente, convolución, operador fraccionario derivativo generalizado.Abstract
The main aim of the present paper is to obtain a new class of multivalent functions which is defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator.We study the region of starlikeness and convexity of the class
. Also we apply the Fractional calculus techniques to obtain the applications of the class . Finally, the familiar concept of δ-neighborhoods of p-valent functions for above mentioned class are employed.
References
[1] Altinas O. and Owa S.: Neighborhoods of certain analytic functions with negative coefficients, Internet J. Math. Sci., 19, pp. 797-800, (1996).
[2] Goyal S.P. and Goyal R.: On a class of multivalent functions defined by generalized Ruscheweyh derivatives involving a general fractional derivative operator, J. Indian Acad. Math., 27 (2), pp. 439-456, (2005).
[3] Kanas K. and Wisniowska A.: Conic regions and k-uniformly convexity II, Folia Sci. Tech.Reso., 170, pp. 65-78, (1998).
[4] Komatu Y.: On analytic prolongation of a family of operators , Mathematica(cluj), 39 (55), pp. 141-145, (1990).
[5] Ravichandran V., Sreenivasagan N. and Srivastava H. M.: Some inequalities associated with linear operator defined for a class of multivalent functions , J. Inequal. Pure Appl. Math., 4 (4), Art.70, pp. 1-7, (2003).
[6] Ruscheweyh S.: Neighborhoods of univalent functions, Proc. Amer. Math.Soc., 81(4), pp. 521-527, (1981).
[7] Shams S. and Kulkarni S. R.: Certain properties of the class of univalent functions defined by Ruscheweyh derivatives, Bull. calcutta Math. Soc., To appear (1997).
[8] Shams, S., Kulkarni, S. R. and Jahangiri, Jay M.: On a class of univalent functions defined by Ruscheweyh derivatives, Kyungpook Math. J., 43, pp. 579-585, (2003).
[9] Silverman H.:Univalent functions with negative coefficient, Proc. Amer.Math.Soc., 51, pp. 109-116, (1975).
[10] Srivastava, H.M.: Distortion inequalities for analytic and univalent functions associated with certain fractional calculus and other linear operators (In Analytic and Geometric Inequalities and Applications eds. T. M. Rassias and H. M. Srivastava), Kluwar Academic Publishers, 478, pp. 349-374, (1999).
[11] Srivastava H. M. and Owa S. (Editors): Current topics in analytic function theory, World Scientific Publishing Company Singapore, pp.36-47, (1992).
[12] Srivastava, H. M. and Saxena, R. K.: Operators of fractional integration and their applications, Applied Mathematics and Computation, 118, pp. 1-52, (2001).
[13] Tehranchi A. and Kulkarni S. R. : Study of the class of univalent functions with negative coefficients defined by Ruscheweyh derivatives. II, J. Raj. Acad. Phy. Sci., 5(1), pp. 105-118, (2006).
[2] Goyal S.P. and Goyal R.: On a class of multivalent functions defined by generalized Ruscheweyh derivatives involving a general fractional derivative operator, J. Indian Acad. Math., 27 (2), pp. 439-456, (2005).
[3] Kanas K. and Wisniowska A.: Conic regions and k-uniformly convexity II, Folia Sci. Tech.Reso., 170, pp. 65-78, (1998).
[4] Komatu Y.: On analytic prolongation of a family of operators , Mathematica(cluj), 39 (55), pp. 141-145, (1990).
[5] Ravichandran V., Sreenivasagan N. and Srivastava H. M.: Some inequalities associated with linear operator defined for a class of multivalent functions , J. Inequal. Pure Appl. Math., 4 (4), Art.70, pp. 1-7, (2003).
[6] Ruscheweyh S.: Neighborhoods of univalent functions, Proc. Amer. Math.Soc., 81(4), pp. 521-527, (1981).
[7] Shams S. and Kulkarni S. R.: Certain properties of the class of univalent functions defined by Ruscheweyh derivatives, Bull. calcutta Math. Soc., To appear (1997).
[8] Shams, S., Kulkarni, S. R. and Jahangiri, Jay M.: On a class of univalent functions defined by Ruscheweyh derivatives, Kyungpook Math. J., 43, pp. 579-585, (2003).
[9] Silverman H.:Univalent functions with negative coefficient, Proc. Amer.Math.Soc., 51, pp. 109-116, (1975).
[10] Srivastava, H.M.: Distortion inequalities for analytic and univalent functions associated with certain fractional calculus and other linear operators (In Analytic and Geometric Inequalities and Applications eds. T. M. Rassias and H. M. Srivastava), Kluwar Academic Publishers, 478, pp. 349-374, (1999).
[11] Srivastava H. M. and Owa S. (Editors): Current topics in analytic function theory, World Scientific Publishing Company Singapore, pp.36-47, (1992).
[12] Srivastava, H. M. and Saxena, R. K.: Operators of fractional integration and their applications, Applied Mathematics and Computation, 118, pp. 1-52, (2001).
[13] Tehranchi A. and Kulkarni S. R. : Study of the class of univalent functions with negative coefficients defined by Ruscheweyh derivatives. II, J. Raj. Acad. Phy. Sci., 5(1), pp. 105-118, (2006).
Published
2017-03-23
How to Cite
[1]
H. S. Parihar and R. Agarwal, “A class of multivalent functions defined by generalized Ruscheweyh derivatives involving a general fractional derivative operator”, Proyecciones (Antofagasta, On line), vol. 33, no. 2, pp. 189-204, Mar. 2017.
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