Quasi-subordination and coefficient bounds for certain classes of meromorphic functions of complex order
Abstract
In this paper, we obtain Fekete-Szegö functional |a₁-μa₀²| for functions of the classes Σ_{q}^{∗}(ϕ) and Σ_{q,λ,b}^{∗}(g,ϕ) using quasi-subordination. Sharp bounds for the Fekete-Szegö functional |a₁-μa₀²| are obtained. Also, applications of the main results for subclasses of functions defined by Bessel function are also considered.
Keywords
Analytic meromorphic starlike function Fekete-Szegö problem convolution subordination quasi-subordination Bessel function
References
- Aouf, M. K., El-Ashwah R. M. and Zayed, H. M., Fekete--Szego inequalities for certain class of meromorphic functions, J. Egyptian Math. Soc., 21 (2013), 197--200.
- Aouf, M. K., Mostafa, A. O. and Zayed, H. M., Convolution properties for some subclasses of meromorphic functions of complex order, Abstr. Appl. Anal., 2015 (2015), 1-6.
- Baricz, A., Generalized Bessel Functions of the First Kind, Lecture Notes in Math., Vol. 1994, Springer-Verlag, Berlin, 2010.
- Baricz, A., Deniz, E., Caglar, M. and Orhan, H., Differential subordinations involving the generalized Bessel functions, Bull. Malays. Math. Sci. Soc., 38 (2015), no. 3, 1255-1280.
- Deniz, E., Differential subordination and superordination results for an operator associated with the generalized Bessel function, Preprint.
- Goyal, S. P. and Goswami, P., Majorization for certain classes of meromorphic functions defined by integral operator, Ann. Univ. Mariae Curie Sklodowska Lublin-Polonia, 2 (2012), 57--62.
- Keogh, F. R. and Merkes, E. P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20 (1969), 8-12.
- Miller, J. E., Convex meromrphic mapping and related functions, Proc. Amer. Math. Soc., 25 (1970), 220-228.
- Miller, S. S. and Mocanu, P. T., Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math., vol. 255, Marcel Dekker, Inc., New York, 2000.
- Mohd, M. H. and Darus, M., Fekete-Szego problems for quasi-subordination classes, Abstr. Appl. Anal., (2012), Art. ID 192956, 1-14.
- Mostafa, A. O., Aouf, M. K. and Zayed, H. M., Convolution properties for some subclasses of meromorphic bounded functions of complex order, Int. J. Open Problems Complex Analysis, 8 (2016), no. 3 , 12-19.
- Nehari, Z., Conformal Mapping, McGraw-Hill, New York, 1952.
- Pommerenke, Ch., On meromrphic starlike functions, Pacific J. Math., 13 (1963), 221-235.
- Robertson, M. S., Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc., 76 (1970), 1-9.
- Silverman, H., Suchithra, K., Stephen, B. A. and Gangadharan, A., Cofficient bounds for certain classes of meromorphic functions, J. Inequal. Pure Appl. Math., (2008), 1-9.
Abstract
References
- Aouf, M. K., El-Ashwah R. M. and Zayed, H. M., Fekete--Szego inequalities for certain class of meromorphic functions, J. Egyptian Math. Soc., 21 (2013), 197--200.
- Aouf, M. K., Mostafa, A. O. and Zayed, H. M., Convolution properties for some subclasses of meromorphic functions of complex order, Abstr. Appl. Anal., 2015 (2015), 1-6.
- Baricz, A., Generalized Bessel Functions of the First Kind, Lecture Notes in Math., Vol. 1994, Springer-Verlag, Berlin, 2010.
- Baricz, A., Deniz, E., Caglar, M. and Orhan, H., Differential subordinations involving the generalized Bessel functions, Bull. Malays. Math. Sci. Soc., 38 (2015), no. 3, 1255-1280.
- Deniz, E., Differential subordination and superordination results for an operator associated with the generalized Bessel function, Preprint.
- Goyal, S. P. and Goswami, P., Majorization for certain classes of meromorphic functions defined by integral operator, Ann. Univ. Mariae Curie Sklodowska Lublin-Polonia, 2 (2012), 57--62.
- Keogh, F. R. and Merkes, E. P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20 (1969), 8-12.
- Miller, J. E., Convex meromrphic mapping and related functions, Proc. Amer. Math. Soc., 25 (1970), 220-228.
- Miller, S. S. and Mocanu, P. T., Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math., vol. 255, Marcel Dekker, Inc., New York, 2000.
- Mohd, M. H. and Darus, M., Fekete-Szego problems for quasi-subordination classes, Abstr. Appl. Anal., (2012), Art. ID 192956, 1-14.
- Mostafa, A. O., Aouf, M. K. and Zayed, H. M., Convolution properties for some subclasses of meromorphic bounded functions of complex order, Int. J. Open Problems Complex Analysis, 8 (2016), no. 3 , 12-19.
- Nehari, Z., Conformal Mapping, McGraw-Hill, New York, 1952.
- Pommerenke, Ch., On meromrphic starlike functions, Pacific J. Math., 13 (1963), 221-235.
- Robertson, M. S., Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc., 76 (1970), 1-9.
- Silverman, H., Suchithra, K., Stephen, B. A. and Gangadharan, A., Cofficient bounds for certain classes of meromorphic functions, J. Inequal. Pure Appl. Math., (2008), 1-9.
Details
| Primary Language | English |
|---|---|
| Journal Section | Review Articles |
| Authors | |
| Publication Date | February 1, 2019 |
| Submission Date | September 12, 2017 |
| Acceptance Date | May 16, 2018 |
| Published in Issue | Year 2019 Volume: 68 Issue: 1 |
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Cited By
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
