Integral Representations and Coefficient Estimates for a Subclass of Meromorphic Starlike Functions
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Abstract
In this paper, we introduce a natural subclass of meromorphic starlike functions in the open unit disk. Results concerning subordination properties, integral representations, properties of convolutions, inclusion relationship and coefficient inequalities for the functions of this class are derived. Furthermore, we solve radius problems for certain related classes of meromorphic strongly starlike functions and meromorphic parabolic starlike functions.
Keywords
Analytic functions Univalent functions Starlike functions Meromorphic starlike functions Meromorphic strongly starlike functions Meromorphic parabolic starlike functions Principle of differential subordination Maximum modulus principleMathematics Subject Classification
Primary 30C45 Secondary 30C50Notes
Acknowledgments
Research was supported by the National Natural Science Foundation of the People’s Republic of China, Grant No. 11371126. A. Rasila received partial support from Academy of Finland (No. 289576). The authors would like to thank the referees for their valuable comments and suggestions, which essentially improved the quality of this paper.
References
- 1.Cho, N.E., Kwon, O.S., Owa, S., Srivastava, H.M.: A class of integral operators preserving subordination and superordination for meromorphic functions. Appl. Math. Comput. 193, 463–474 (2007)MathSciNetzbMATHGoogle Scholar
- 2.Kuroki, K., Owa, S.: Notes on new class for certain analytic functions. RIMS Kôkyûroku 1772, 21–25 (2011)Google Scholar
- 3.Kwon, O.S., Sim, Y.J., Cho, N.E., Srivastava, H.M.: Some radius problems related to a certain subclass of analytic functions. Acta Math. Sin. (Engl. Ser.) 30, 1133–1144 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
- 4.Liu, J.-L., Srivastava, H.M.: Some convolution conditions for starlikeness and convexity of meromorphically multivalent functions. Appl. Math. Lett. 16, 13–16 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
- 5.Miller, J.: Convex and starlike meromorphic functions. Proc. Am. Math. Soc. 80, 607–613 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
- 6.Arif, M.: On sufficient conditions of meromorphic starlike functions. Bol. Soc. Paranaense Mat. 32, 229–236 (2014)MathSciNetGoogle Scholar
- 7.Nunokawa, M., Ahuja, O.P.: On meromorphic starlike and convex functions. Indian J. Pure Appl. Math. 32, 1027–1032 (2001)MathSciNetzbMATHGoogle Scholar
- 8.Rogosinski, W.: On the coefficients of subordinate functions. Proc. London Math. Soc. 48, 48–82 (1943)MathSciNetzbMATHGoogle Scholar
- 9.Sim, Y.J., Kwon, O.S.: On certain classes of convex functions. Int. J. Math. Math. Sci. (2013) (Article ID 294378, 1–6)Google Scholar
- 10.Sun, Y., Jiang, Y.-P., Rasila, A.: Coefficient estimates for certain subclasses of analytic and bi-univalent functions. Filomat 29, 351–360 (2015)MathSciNetCrossRefGoogle Scholar
- 11.Sun, Y., Kuang, W.-P., Wang, Z.-G.: On meromorphic starlike functions of reciprocal order \(\alpha \). Bull. Malays. Math. Sci. Soc. (Ser. 2) 35, 469–477 (2012)MathSciNetzbMATHGoogle Scholar
- 12.Wang, Z.-G., Liu, Z.-H., Xiang, R.-G.: Some criteria for meromorphic multivalent starlike functions. Appl. Math. Comput. 218, 1107–1111 (2011)MathSciNetzbMATHGoogle Scholar
- 13.Wang, Z.-G., Srivastava, H. M., Yuan, S.-M.: Some basic properties of certain subclasses of meromorphically starlike functions. J. Inequal. Appl. 2014, 1–13 (2014)Google Scholar
- 14.Wang, Z.-G., Sun, Y., Zhang, Z.-H.: Certain classes of meromorphic multivalent functions. Comput. Math. Appl. 58, 1408–1417 (2009)MathSciNetCrossRefzbMATHGoogle Scholar