Abstract
The object of the present paper is to investigate some inclusion relationships and a number of other properties of several subclasses of multivalent analytic functions, which are defined here by using the hypergeometric function. Relevant connections of the results presented here with those obtained in earlier works are pointed out.
References
[1] Al-KHARSANI, H. A.-Al-AREEFI, N. M.: On classes of multivalent functions involving linear operator and multiplier transformations, Hacettepe J. Math. Stat. 37 (2008), 115-127.Suche in Google Scholar
[2] BULBOACA, T.: Differential Subordinations and Superordinations. Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.Suche in Google Scholar
[3] CARLSON, B. C.-SHAFFER, D. B.: Starlike and prestarlike hypergeometric function, SIAM J. Math. Anal. 15 (1984), 737-745.10.1137/0515057Suche in Google Scholar
[4] CHO, N. E.-KWON, O. H.-SRIVASTAVA, H. M.: Inclusion and argument properties for certain subclass of multivalent functions associated with a family of linear operator, J. Math. Anal. Appl. 292 (2004), 470-483.10.1016/j.jmaa.2003.12.026Suche in Google Scholar
[5] CHOI, J. H.-SAIGO, M.-SRIVASTAVA, H. M.: Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002), 432-445.10.1016/S0022-247X(02)00500-0Suche in Google Scholar
[6] HALLENBECK, D. J.-RUSCHEWEYH, St.: Subordination by convex functions, Proc. Amer. Math. Soc. 52 (1975), 191-195. 10.1090/S0002-9939-1975-0374403-3Suche in Google Scholar
[7] KANAS, S.: Techniques of the differential subordination for domains bounded by conic sections, Int. J. Math. Math. Sci. 38 (2003), 2389-2400.10.1155/S0161171203302212Suche in Google Scholar
[8] KANAS, S.-KOWALCZYK, J.: A note on Briot-Bouquet-Bernoulli differential subordination, Comment. Math. Univ. Carolin. 46 (2005), 1-10.Suche in Google Scholar
[9] KANAS, S.-LECKO, A.-STANKIEWICZ, J.: Differential subordination and geometric means, Complex Variables Theory Appl. 18 (1995), 201-209.Suche in Google Scholar
[10] VINOD KUMAR-SHUKLA, S. L.: Multivalent functions defined by Ruscheweyh derivatives. I; II, Indian J. Pure Appl. Math. 15 (1984), 1216-1227; 1228-1238.Suche in Google Scholar
[11] KWON, O. S.-CHO, N. E.: Inclusion properties for certain subclasses of analytic functions associated with the Dziok-Srivastava operator, J. Ineq. Appl. Vol. (2007), Art. ID51079, 1-10.Suche in Google Scholar
[12] LASHIN, A. Y.: Some convolution properties of analytic functions, Appl. Math. Lett. 18 (2005), 135-138.10.1016/j.aml.2004.09.003Suche in Google Scholar
[13] LIU, M.-S.: On certain sufficient condition for starlike functions, Soochow. J. Math. 29 (2003), 407-412.Suche in Google Scholar
[14] LIU, J.-L.-NOOR, K. I.: Some properties of Noor integral operator, J. Natur. Geom. 21 (2002), 81-90.Suche in Google Scholar
[15] MILLER, S. S.-MOCANU, P. T.: Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 157-171.10.1307/mmj/1029002507Suche in Google Scholar
[16] MILLER, S. S. -MOCANU, P. T.: Univalent solutions of Briot-Bouquet differential equations, J. Differential Equarions 56 (1985), 297-309.10.1016/0022-0396(85)90082-8Suche in Google Scholar
[17] MILLER, S. S.-MOCANU, P. T.: Differential Subordinations: Theory and Applications. Ser. on Monographs and Texbooks in Pure and Appl. Math., Vol. 225, Marcel Dekker, New York-Basel, 2000.10.1201/9781482289817Suche in Google Scholar
[18] OBRADOVIC, M.-OWA, S.: On certain properties for some classes of starlike functions, J. Math. Anal. Appl. 145 (1990), 357-364.10.1016/0022-247X(90)90405-5Suche in Google Scholar
[19] PASHKOULEVA, D. Z.: The starlikeness and spiral-convexity of certain subclasses of analytic functions. In: Current Topics in Analytic Function Theory (H. M. Srivastava, S. Owa, eds.), World Scientific Publishing, Hong Kong, 1992, pp. 266-273.Suche in Google Scholar
[20] PATEL, J.-MISHRA, A. K.-SRIVASTAVA, H. M.: Classes of multivalent analytic functions involving the Dziok-Srivastava operator, Comput. Math. Appl. 54 (2007), 599-616.10.1016/j.camwa.2006.08.041Suche in Google Scholar
[21] PATEL, J.-CHO, N. E.-SRIVASTAVA, H. M.: Certain subclasses of multivalent functions associated with a family of linear operator, Math. Comput. Modelling 43 (2006), 320-338.10.1016/j.mcm.2005.06.014Suche in Google Scholar
[22] RUSCHEWEYH, S.-SHEIL-SMALL, T.: Hadamard products of schlicht functions and the poloya-schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119-135.10.1007/BF02566116Suche in Google Scholar
[23] SAITOH, H.: A linear operator and its applications of first order differential subordinations, Math. Japon. 44 (1996), 31-38.Suche in Google Scholar
[24] SRIVASTAVA, H. M.-KARLSSON, P. W.: Multiple Gausian Hypergeometric Series, Halsted Press, Ellis Horwood Limited, Chichester/John Wiley and Sons, New York- Chichester-Brisbane-London, 1985.Suche in Google Scholar
[25] STANKIEWICZ, J.-STANKIEWICZ, Z.: Some applications of the Hadamard convolution in the theory of functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A 40 (1986), 251-265. 531Suche in Google Scholar
[26] WHITTAKER, E. T.-WASTSON, G. N.: A Course on Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcenclental Functions (4th ed. Reprinted), Cambridge Univ. Press, Camridge, 1927.Suche in Google Scholar
© Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Fuzzy Pseudo Subalgebras and Ideals of Pseudo D-Algebras
- Five Curious Congruences Modulo p2
- On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums
- Constructing New Crossed Group Categories Over Weak Hopf Group Algebras
- Generalization of Hilbert Inequality with Some Parameters
- Some Applications of Differential Subordination of p-Valent Functions
- Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions
- On Properties of Entire Solutions of Difference Equations and Difference Polynomials
- On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations
- On the Existence of Solutions of Ordinary Differential Equations in Banach Spaces
- Global Dynamics of a Delayed n + m-Species Competition Predator-Prey System on Time Scales
- Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System
- A Generalization of Cyclic Amenability of Banach Algebras
- n-Weak Module Amenability of Triangular Banach Algebras
- On a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space
- Optimality Conditions for Vector Equilibrium Problems with Set-Valued Mappings and Cone Constraints
- Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms
- A New Proof of a Theorem on Long Cycles
Artikel in diesem Heft
- Fuzzy Pseudo Subalgebras and Ideals of Pseudo D-Algebras
- Five Curious Congruences Modulo p2
- On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums
- Constructing New Crossed Group Categories Over Weak Hopf Group Algebras
- Generalization of Hilbert Inequality with Some Parameters
- Some Applications of Differential Subordination of p-Valent Functions
- Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions
- On Properties of Entire Solutions of Difference Equations and Difference Polynomials
- On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations
- On the Existence of Solutions of Ordinary Differential Equations in Banach Spaces
- Global Dynamics of a Delayed n + m-Species Competition Predator-Prey System on Time Scales
- Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System
- A Generalization of Cyclic Amenability of Banach Algebras
- n-Weak Module Amenability of Triangular Banach Algebras
- On a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space
- Optimality Conditions for Vector Equilibrium Problems with Set-Valued Mappings and Cone Constraints
- Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms
- A New Proof of a Theorem on Long Cycles