A Criterion for Subfamilies of Multivalent Functions of Reciprocal Order with Respect to Symmetric Points
Abstract
:1. Introduction
2. Main Results
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
- Miller, S.S.; Mocanu, P.T. Differential subordinations and inequalities in the complex plane. J. Differ. Equ. 1987, 67, 199–211. [Google Scholar] [CrossRef] [Green Version]
- Uralegaddi, B.A.; Ganigi, M.D.; Sarangi, S.M. Univalent functions with positive coefficients. Tamkang J. Math. 1994, 25, 225–230. [Google Scholar]
- Owa, S.; Nishiwaki, J. Coefficient estimates for certain classes of analytic functions. J. Ineq. Pure Appl. Math. 2002, 3, 72. [Google Scholar]
- Nunokawa, M.; Owa, S.; Polattoglu, Y.; Caglar, M.; Duman, E.Y. Some sufficient conditions for starlikeness and convexity. Turk. J. Math. 2010, 34, 333–337. [Google Scholar]
- Owa, S.; Srivastava, H.M. Some generalized convolution properties associated with certain subclasses of analytic functions. J. Ineq. Pure Appl. Math. 2002, 3, 42. [Google Scholar]
- Polatoğlu, Y.; Blocal, M.; Sen, A.; Yavuz, E. An investigation on a subclass of p-valently starlike functions in the unit disc. Turk. J. Math. 2007, 31, 221–228. [Google Scholar]
- Dixit, K.K.; Pathak, A.L. A new class of analytic functions with positive coefficients. Ind. J. Pure. Appl. Math. 2003, 34, 209–218. [Google Scholar]
- Uyanik, N.; Shiraishi, H.; Owa, S.; Polatoğlu, Y. Reciprocal classes of p-valently spirallike and p-valently Robertson functions. J. Ineq. Appl. 2011, 2011, 61. [Google Scholar] [CrossRef]
- Arif, M.; Umar, S.; Mahmood, S.; Sokol, J. New reciprocal class of analytic functions associated with linear operator. Iran. J. Sci. Technol. Trans. A Sci. 2018, 42, 881. [Google Scholar] [CrossRef]
- Arif, M. Sufficiency criteria for a class of p-valent analytic functions of complex order. Abstr. Appl. Anal. 2013, 2013, 517296. [Google Scholar] [CrossRef]
- Ponnusamy, S.; Singh, V. Criteria for strongly starlike functions. Complex Var. Theory Appl. 1997, 34, 267–291. [Google Scholar] [CrossRef]
- Ravichandran, V.; Selvaraj, C.; Rajalakshami, R. Sufficient conditions for starlike functions of order α. J. Ineq. Pure Appl. Math. 2002, 3, 81. [Google Scholar]
- Sokół, J.; Spelina, L.T. On a sufficient condition for strongly starlikeness. J. Ineq. Appl. 2013, 2013, 383. [Google Scholar] [CrossRef] [Green Version]
- Uyanik, N.; Aydogan, M.; Owa, S. Extension of sufficient conditions for starlikeness and convexity of order α. Appl. Math. Lett. 2011, 24, 1393–1399. [Google Scholar] [CrossRef]
- Yang, D.-G. Some criteria for multivalently starlikeness. Southeast Asian Bull. Math. 2000, 24, 491–497. [Google Scholar] [CrossRef]
- Arif, M.; Ayaz, M.; Aouf, M.K. New criteria for functions to be in a class of p -valent alpha convex functions. Sci. World J. 2013, 2013, 280191. [Google Scholar] [CrossRef] [PubMed]
- Arif, M.; Ayaz, M.; Iqbal, J.; Haq, W. Sufficient conditions for functions to be in a class of p -valent analytic functions. J. Comput. Anal. Appl. 2013, 16, 159–164. [Google Scholar]
- Jack, I.S. Functions starlike and convex of order α. J. Lond. Math. Soc. 1971, 3, 469–474. [Google Scholar] [CrossRef]
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Mahmood, S.; Srivastava, H.M.; Arif, M.; Ghani, F.; AbuJarad, E.S.A. A Criterion for Subfamilies of Multivalent Functions of Reciprocal Order with Respect to Symmetric Points. Fractal Fract. 2019, 3, 35. https://doi.org/10.3390/fractalfract3020035
Mahmood S, Srivastava HM, Arif M, Ghani F, AbuJarad ESA. A Criterion for Subfamilies of Multivalent Functions of Reciprocal Order with Respect to Symmetric Points. Fractal and Fractional. 2019; 3(2):35. https://doi.org/10.3390/fractalfract3020035
Chicago/Turabian StyleMahmood, Shahid, Hari Mohan Srivastava, Muhammad Arif, Fazal Ghani, and Eman S. A. AbuJarad. 2019. "A Criterion for Subfamilies of Multivalent Functions of Reciprocal Order with Respect to Symmetric Points" Fractal and Fractional 3, no. 2: 35. https://doi.org/10.3390/fractalfract3020035