The object of this paper is to investigate some inclusion relationships and a number of other useful properties among certain subclasses of analytic and $p$-valent functions, which are defined here by certain integral operator.
References
J.H. Choi, M. Saigo and H.M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002), 432–445. MR1944360 1035.30004 10.1016/S0022-247X(02)00500-0 J.H. Choi, M. Saigo and H.M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002), 432–445. MR1944360 1035.30004 10.1016/S0022-247X(02)00500-0
T.B. Jung, Y.C. Kim and H.M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operator, J. Math. Anal. Appl. 176 (1993), 138–147. MR1222160 0774.30008 10.1006/jmaa.1993.1204 T.B. Jung, Y.C. Kim and H.M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operator, J. Math. Anal. Appl. 176 (1993), 138–147. MR1222160 0774.30008 10.1006/jmaa.1993.1204
M.-S. Liu, On certain sufficient condition for starlike functions, Soochow J. Math. 29 (2003), 407–412. MR2021540 1043.30007 M.-S. Liu, On certain sufficient condition for starlike functions, Soochow J. Math. 29 (2003), 407–412. MR2021540 1043.30007
S.S. Miller and P.T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289–305. MR506307 0367.34005 10.1016/0022-247X(78)90181-6 S.S. Miller and P.T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289–305. MR506307 0367.34005 10.1016/0022-247X(78)90181-6
S.S. Miller and P.T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 157–171. MR616267 10.1307/mmj/1029002507 euclid.mmj/1029002507
S.S. Miller and P.T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 157–171. MR616267 10.1307/mmj/1029002507 euclid.mmj/1029002507
S.S. Miller and P.T. Mocanu, Differential subordinations. Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math. No. 225, Marcel Dekker Inc., New York, 2000. MR1760285 S.S. Miller and P.T. Mocanu, Differential subordinations. Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math. No. 225, Marcel Dekker Inc., New York, 2000. MR1760285
P.T. Mocanu and Gh. Oros, A sufficient condtion for starlikeness of order $\alpha$, Int. J. Math. Math. Sci. 28 (2001), no. 9, 557–560. MR1895302 1085.30501 10.1155/S0161171201011656 P.T. Mocanu and Gh. Oros, A sufficient condtion for starlikeness of order $\alpha$, Int. J. Math. Math. Sci. 28 (2001), no. 9, 557–560. MR1895302 1085.30501 10.1155/S0161171201011656
D.Z. Pashkouleva, The starlikeness and spiral-convxity of certain subclasses of analytic, in: H. M. Srivastava and S. Owa (Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1992. MR1232446 1002.30500 D.Z. Pashkouleva, The starlikeness and spiral-convxity of certain subclasses of analytic, in: H. M. Srivastava and S. Owa (Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1992. MR1232446 1002.30500
J. Patel, A.K. Mishra and H.M. Srivastava, Classes of multivant analytic functions involving the Dziok-Srivastava operator, Comput. Math. Appl. 54 (2007), 599–616. MR2345915 J. Patel, A.K. Mishra and H.M. Srivastava, Classes of multivant analytic functions involving the Dziok-Srivastava operator, Comput. Math. Appl. 54 (2007), 599–616. MR2345915
S. Shams, S. R. Kulkarni and J.M. Jahangiri, Subordination properties for $p$-valent functions defined by integral operators, Int. J. Math. Math. Sci., Vol. 2006, Article ID 94572, 1–3. MR2172796 1137.30006 10.1155/IJMMS/2006/94572 S. Shams, S. R. Kulkarni and J.M. Jahangiri, Subordination properties for $p$-valent functions defined by integral operators, Int. J. Math. Math. Sci., Vol. 2006, Article ID 94572, 1–3. MR2172796 1137.30006 10.1155/IJMMS/2006/94572
J. Stankiewicz and Z. Stankiewicz, Some applications of the Hadamard convolution in the theory of functions, Ann. Univ. Mariae Curie-Skłodwska Sect. A 40 (1986), 251–265. MR945178 0642.30019 J. Stankiewicz and Z. Stankiewicz, Some applications of the Hadamard convolution in the theory of functions, Ann. Univ. Mariae Curie-Skłodwska Sect. A 40 (1986), 251–265. MR945178 0642.30019
E.T. Whittaker and G.N. Watson, A Course on Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions with an Account of the Principal Transcendental Functions, Fourth Edition, Cambridige Univ. Press, Camridge, 1927. MR1424469 E.T. Whittaker and G.N. Watson, A Course on Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions with an Account of the Principal Transcendental Functions, Fourth Edition, Cambridige Univ. Press, Camridge, 1927. MR1424469
