Ali, R. M., Badghaish, A. O. and Ravichandran, V. Subordination for higher-order deriva- tives of multivalent functions, J. Ineq. Appl. 2008, Art. ID 830138, 1-12, 2008.
Altinatas, O. Neighborhoods of certain subclasses of p-valently analytic functions with neg- ative coefficients, Appl. Math. Comput. 187 (1), 47–53, 2007.
Altinatas, O., Irmak, H. and Srivastava, H. M. Neighborhoods for certain subclasses of mul- tivalently analytic functions defined by differential operator, Comput. Math. Appl. 55 (9), 331–338, 2008.
Aouf, M. K., Al-Oboudi, F. M. and Hidan, M. M. On some results for λ-spirallike and λ- Robertson functions of complex order, Publ. Institute Math. Belgrade 77 (91), 93–98, 2005. [5] Bulboaca, T. Differential Subordinations and Superordinations, Recent Results (House of Scientific Book Publ., Cluj-Napoca, 2005).
Chen, M.P., Irmak, H. and Srivastava, H. M. Some multivalent functions with negative coefficients defined by using a differential operator, PanAmerc. Math. J. 6 (2), 55–64, 1996. [7] El-Ashwah, R. M. Inclusion and neighborhood properties of a certain subclasses of p-valent functions with negative coefficients, Filomat 23 (3), 1–13, 2009.
Frasin, B. A. Neighborhoods of certain multivalent analytic functions with negative coeffi- cients, Appl. Math. Comput. 193 (1), 1–6, 2007.
Irmak, H. A class of p-valently analytic function with positive coefficients, Tamkang J. of Math. 27 (4), 315–322, 1996.
Irmak, H. and Cho, N. E. A differential operator and its applications to certain multivalently analytic functions, Hacet. J. Math. Stat. 36 (1), 1–6, 2007.
Irmak, H., Lee, S. H. and Cho, N. E. Some multivalently starlike functions with negative coefficients and their subclasses defined by using a differential operator, Kyungpook Math. J. 37 (1), 43–51, 1997.
Miller, S. S. and Mocanu, P. T. Differential subordinations: Theory and Applications (Series on Mongraphs and Textbooks in Pure and Applied Mathematics 225, Marcel Dekker Inc., New York. and Basel, 2000).
Miller, S. S. and Mocanu, P. T. Subordinants of differential superordinations, Complex Vari- ables 48 (10), 815–826, 2003.
Murugusundaramoorthy, G. and Magesh, N. Differential subordinations and superordina- tions for analytic functions defined by the Dziok-Srivastava linear operator, J. Inequal. Pure Appl. Math. 7 (4), Art. 152, 1–9, 2006.
Nunokawa, M. On the multivalent function, Indian J. Pure Appl. Math. 20 (6), 577–582, 1989. [16] Obradovic, M. and Owa, S. On certain properties for some classes of starlike functions, J. Math. Anal. Appl. 145, 357–364, 1990.
Polatoglu, Y. Some result of analytic function in the unit disc, Publications de l’Institut Math. 78 (92), 79–85, 2005.
Royster, W. C. On the univalence of a certain integral, Michigan Math. J. 12, 385–387, 1965. [19] Shanmugam, T. N., Sivasubramanian, S., Darus, M. and Ramachandran, C. Subordination and superordination results for subclasses of analytic functions, Internat. J. Math. Forum 2(21), 1039–1052, 2007.
Silverman, H. Higher order derivatives, Chinese J. of Math. 23 (2), 189–191, 1995.
Srivastava, H. M. and Lashin, A. Y. Some applications of the Briot-Bouquet differential subordination, J. Inequal. Pure. Appl. Math. 6 (2), Art. 41, 1–7, 2005.
Yaguchi, T. The radii of starlikeness and convexity for certain multivalent functions, in: Current Topics in Analytic Function Theory, (Edited by H. M. Srivastava and S. Owa) (World Scientific, River Edge, NJ, USA, 1992) 375-386.
Subordination and Superordination for Higher-Order Derivatives of p-Valent Analytic Functions
Year 2011,
Volume: 40 Issue: 4, 493 - 502, 01.04.2011
Ali, R. M., Badghaish, A. O. and Ravichandran, V. Subordination for higher-order deriva- tives of multivalent functions, J. Ineq. Appl. 2008, Art. ID 830138, 1-12, 2008.
Altinatas, O. Neighborhoods of certain subclasses of p-valently analytic functions with neg- ative coefficients, Appl. Math. Comput. 187 (1), 47–53, 2007.
Altinatas, O., Irmak, H. and Srivastava, H. M. Neighborhoods for certain subclasses of mul- tivalently analytic functions defined by differential operator, Comput. Math. Appl. 55 (9), 331–338, 2008.
Aouf, M. K., Al-Oboudi, F. M. and Hidan, M. M. On some results for λ-spirallike and λ- Robertson functions of complex order, Publ. Institute Math. Belgrade 77 (91), 93–98, 2005. [5] Bulboaca, T. Differential Subordinations and Superordinations, Recent Results (House of Scientific Book Publ., Cluj-Napoca, 2005).
Chen, M.P., Irmak, H. and Srivastava, H. M. Some multivalent functions with negative coefficients defined by using a differential operator, PanAmerc. Math. J. 6 (2), 55–64, 1996. [7] El-Ashwah, R. M. Inclusion and neighborhood properties of a certain subclasses of p-valent functions with negative coefficients, Filomat 23 (3), 1–13, 2009.
Frasin, B. A. Neighborhoods of certain multivalent analytic functions with negative coeffi- cients, Appl. Math. Comput. 193 (1), 1–6, 2007.
Irmak, H. A class of p-valently analytic function with positive coefficients, Tamkang J. of Math. 27 (4), 315–322, 1996.
Irmak, H. and Cho, N. E. A differential operator and its applications to certain multivalently analytic functions, Hacet. J. Math. Stat. 36 (1), 1–6, 2007.
Irmak, H., Lee, S. H. and Cho, N. E. Some multivalently starlike functions with negative coefficients and their subclasses defined by using a differential operator, Kyungpook Math. J. 37 (1), 43–51, 1997.
Miller, S. S. and Mocanu, P. T. Differential subordinations: Theory and Applications (Series on Mongraphs and Textbooks in Pure and Applied Mathematics 225, Marcel Dekker Inc., New York. and Basel, 2000).
Miller, S. S. and Mocanu, P. T. Subordinants of differential superordinations, Complex Vari- ables 48 (10), 815–826, 2003.
Murugusundaramoorthy, G. and Magesh, N. Differential subordinations and superordina- tions for analytic functions defined by the Dziok-Srivastava linear operator, J. Inequal. Pure Appl. Math. 7 (4), Art. 152, 1–9, 2006.
Nunokawa, M. On the multivalent function, Indian J. Pure Appl. Math. 20 (6), 577–582, 1989. [16] Obradovic, M. and Owa, S. On certain properties for some classes of starlike functions, J. Math. Anal. Appl. 145, 357–364, 1990.
Polatoglu, Y. Some result of analytic function in the unit disc, Publications de l’Institut Math. 78 (92), 79–85, 2005.
Royster, W. C. On the univalence of a certain integral, Michigan Math. J. 12, 385–387, 1965. [19] Shanmugam, T. N., Sivasubramanian, S., Darus, M. and Ramachandran, C. Subordination and superordination results for subclasses of analytic functions, Internat. J. Math. Forum 2(21), 1039–1052, 2007.
Silverman, H. Higher order derivatives, Chinese J. of Math. 23 (2), 189–191, 1995.
Srivastava, H. M. and Lashin, A. Y. Some applications of the Briot-Bouquet differential subordination, J. Inequal. Pure. Appl. Math. 6 (2), Art. 41, 1–7, 2005.
Yaguchi, T. The radii of starlikeness and convexity for certain multivalent functions, in: Current Topics in Analytic Function Theory, (Edited by H. M. Srivastava and S. Owa) (World Scientific, River Edge, NJ, USA, 1992) 375-386.
El-ashwah, R., & Aouf, M. (2011). Subordination and Superordination for Higher-Order Derivatives of p-Valent Analytic Functions. Hacettepe Journal of Mathematics and Statistics, 40(4), 493-502.
AMA
El-ashwah R, Aouf M. Subordination and Superordination for Higher-Order Derivatives of p-Valent Analytic Functions. Hacettepe Journal of Mathematics and Statistics. April 2011;40(4):493-502.
Chicago
El-ashwah, R.m., and M.k. Aouf. “Subordination and Superordination for Higher-Order Derivatives of P-Valent Analytic Functions”. Hacettepe Journal of Mathematics and Statistics 40, no. 4 (April 2011): 493-502.
EndNote
El-ashwah R, Aouf M (April 1, 2011) Subordination and Superordination for Higher-Order Derivatives of p-Valent Analytic Functions. Hacettepe Journal of Mathematics and Statistics 40 4 493–502.
IEEE
R. El-ashwah and M. Aouf, “Subordination and Superordination for Higher-Order Derivatives of p-Valent Analytic Functions”, Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 4, pp. 493–502, 2011.
ISNAD
El-ashwah, R.m. - Aouf, M.k. “Subordination and Superordination for Higher-Order Derivatives of P-Valent Analytic Functions”. Hacettepe Journal of Mathematics and Statistics 40/4 (April 2011), 493-502.
JAMA
El-ashwah R, Aouf M. Subordination and Superordination for Higher-Order Derivatives of p-Valent Analytic Functions. Hacettepe Journal of Mathematics and Statistics. 2011;40:493–502.
MLA
El-ashwah, R.m. and M.k. Aouf. “Subordination and Superordination for Higher-Order Derivatives of P-Valent Analytic Functions”. Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 4, 2011, pp. 493-02.
Vancouver
El-ashwah R, Aouf M. Subordination and Superordination for Higher-Order Derivatives of p-Valent Analytic Functions. Hacettepe Journal of Mathematics and Statistics. 2011;40(4):493-502.