[1] S. D. Bernardi, New distortion theorems for functions of positive real part and applications to the partial sums of univalent convex functions, Proc. Amer. Math. Soc., 45(1974), no. 1, 113-118.
[2] T. Bulboaca, Di¤erential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.
[3] D. J. Hallenbeck and S. Ruschewyh, Subordination by convex functions, Proc. Amer. Math. Soc., 52 (1975), 191-195.
[4] M.-S. Liu, On certain subclass of analytic functions, J. South China Normal Univ., 4(2002),15-20 (in Chinese).
[5] M. Liu, On certain subclass of pvalent functions, Soochow J. Math., 26(2000), no. 2, 163-171.
[6] S. S. Miller and P.T. Mocanu, Subordinats of di¤erential superordinations, Complex Var., 48(2003), 815-826.
[7] S. S. Miller and P.T. Mocanu, Di¤erential Subordination: Theory and Applications, in: Series in Pure and Applied Mathematics, vol. 225, Marcel Dekker, New York, 2000.
[8] S. Owa and M. Obradovic, Certain subclasses of Bazilevic functions of type, Internat. J. Math. and Math. Sci., 9(1986), no. 2, 97-105.
[9] S. Owa, On certain Bazilevic functions of order , Internat. J. Math. and Math. Sci., 15(1992), no. 3, 613-616.
[10] S. Ponnusamy and S. Rajasekaran, New su¢ cient conditions for starlike and univalent functions, Soochow J. Math., 21(1995), no. 1, 193-201.
[11] T. N. Shanmugam, V. Ravichandran and S. Sivasubramanian, Di¤erential sandwich theorems for subclasses of analytic functions, Australian J. Math. Anal. Appl., 3(2006), Art. 8, 1-11.
[12] R. Singh, On Bazilevic functions, Proc. Amer. Math. Sci., 38(1973), 261-267.
[13] D. G. Yang, Properties of certain classes of multivalent functions, Bull. Inst. Math. Acad. Sinica, 22(1994), no. 4, 361-367.
[14] E. T. Whittaker and G. N.Watson, A Course of Modern Analysis: An Introduction to the General Theory of In…nite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions, Cambridge University Press, Cambridge, 1927.
Some Results of Certain Class of Multivalently Bavilevic Functions
Year 2020,
Volume: 8 Issue: 1, 21 - 29, 15.04.2020
By making use of the principle of subordination, we introduce a certain class of multivalent analytic Bavilevic functions. Also, we obtain subordination and superordination properties, distortion theorems and inequality properties are proved. The results presented here would provide extensions of those given in earlier works.
[1] S. D. Bernardi, New distortion theorems for functions of positive real part and applications to the partial sums of univalent convex functions, Proc. Amer. Math. Soc., 45(1974), no. 1, 113-118.
[2] T. Bulboaca, Di¤erential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.
[3] D. J. Hallenbeck and S. Ruschewyh, Subordination by convex functions, Proc. Amer. Math. Soc., 52 (1975), 191-195.
[4] M.-S. Liu, On certain subclass of analytic functions, J. South China Normal Univ., 4(2002),15-20 (in Chinese).
[5] M. Liu, On certain subclass of pvalent functions, Soochow J. Math., 26(2000), no. 2, 163-171.
[6] S. S. Miller and P.T. Mocanu, Subordinats of di¤erential superordinations, Complex Var., 48(2003), 815-826.
[7] S. S. Miller and P.T. Mocanu, Di¤erential Subordination: Theory and Applications, in: Series in Pure and Applied Mathematics, vol. 225, Marcel Dekker, New York, 2000.
[8] S. Owa and M. Obradovic, Certain subclasses of Bazilevic functions of type, Internat. J. Math. and Math. Sci., 9(1986), no. 2, 97-105.
[9] S. Owa, On certain Bazilevic functions of order , Internat. J. Math. and Math. Sci., 15(1992), no. 3, 613-616.
[10] S. Ponnusamy and S. Rajasekaran, New su¢ cient conditions for starlike and univalent functions, Soochow J. Math., 21(1995), no. 1, 193-201.
[11] T. N. Shanmugam, V. Ravichandran and S. Sivasubramanian, Di¤erential sandwich theorems for subclasses of analytic functions, Australian J. Math. Anal. Appl., 3(2006), Art. 8, 1-11.
[12] R. Singh, On Bazilevic functions, Proc. Amer. Math. Sci., 38(1973), 261-267.
[13] D. G. Yang, Properties of certain classes of multivalent functions, Bull. Inst. Math. Acad. Sinica, 22(1994), no. 4, 361-367.
[14] E. T. Whittaker and G. N.Watson, A Course of Modern Analysis: An Introduction to the General Theory of In…nite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions, Cambridge University Press, Cambridge, 1927.