The Fekete-Szegö estimates for a new class of analytic functions associated with the convolution
Abstract
In the present investigation, we discuss the sharpness of the bound of the Fekete-Szego functional |a3 − µa2 2 | for the functions belonging to certain subclass Rǫ ν,Lg (ψ) of analytic functions by means of convolution. The significant and useful consequences with the relevance of this class with some known classes are also pointed out.
Downloads
References
Agarwal, R., Paliwal, G.S. and Purohit, S.D Geometric properties for an unified class of functions characterized using Fractional Ruscheweyh-Goyal derivative operator, Sci. Tech. Asia, 25(1), 72-84, (2020).
Agarwal, R. and Paliwal, G.S. On the Fekete-Szeg¨o problem for certain subclass of analytic functions, Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, Springer India, 353-361, (2012). https://doi.org/10.1007/978-81-322-1602-5_39 DOI: https://doi.org/10.1007/978-81-322-1602-5_39
Al-Shaqsi, K. and Darus, M., On certain subclasses of analytic functions defined by a multiplier transformation with two parameters, Appl. Math. Sci. 3(36), 1799-1810, (2009).
Ali, R. M., Ravichandran, V. and Seenivasagan, N., Coefficient bounds for p- valent functions, Appl. Math. Comput. 187(1), 35-46, (2007). https://doi.org/10.1016/j.amc.2006.08.100 DOI: https://doi.org/10.1016/j.amc.2006.08.100
Bansal, D., Fekete-Szego problem for a new class of analytic functions, Int. J. Math. Math. Sci. Article ID 143096, 5 pages,(2011). https://doi.org/10.1155/2011/143096 DOI: https://doi.org/10.1155/2011/143096
C?atas, ,A., Oros, G. I. and Oros, G. Differential subordinations associated with multiplier transformations, Abstract Appl. Anal. 2008, ID 845724, 1-11, (2008). https://doi.org/10.1155/2008/845724 DOI: https://doi.org/10.1155/2008/845724
Cho, N. E. and Kim, T. H., Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc. 40(3), 399-410, (2003). https://doi.org/10.4134/BKMS.2003.40.3.399 DOI: https://doi.org/10.4134/BKMS.2003.40.3.399
Cho, N. E. and Srivastava, H. M., Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Model. 37 (1-2), 39-49, (2003). https://doi.org/10.1016/S0895-7177(03)80004-3 DOI: https://doi.org/10.1016/S0895-7177(03)80004-3
Darus, M. and Al-Shaqsi, K., On subordinations for certain analytic functions associated with generalized integral operator, Lobachevskii J. Math. 29, 90-97, (2008). https://doi.org/10.1134/S1995080208020078 DOI: https://doi.org/10.1134/S1995080208020078
Fekete, M. and Szego, G., Eine Bemerkung ¨uber ungerade schlichte funktionen, J. Londan Math. Soc. 8, 85-89, (1933). https://doi.org/10.1112/jlms/s1-8.2.85 DOI: https://doi.org/10.1112/jlms/s1-8.2.85
Jahangiri, J. M., Ramchandran, C. and Annamalai, S., Fekete-Szego problem for certain analytic functions defined by Hypergeometric functions and Jacobi Polynomial, J. Fract. Calc. Appl. 9(1), 1-7, (2018).
Jian Lin, L., On some classes of analytic functions, Math. Jpn., 40(3), 523-529, (1994).
Jung, I. B., Kim, Y. C. and Srivastava, H. M., The Hardy space of analytic functions associated with certain oneparameter families of integral operators, J. Math. Anal. Appl. 176, 138-147, (1993). https://doi.org/10.1006/jmaa.1993.1204 DOI: https://doi.org/10.1006/jmaa.1993.1204
Kant, S. and Vyas, P. P., Sharp bounds of Fekete-Szego functional for quasi-subordination class, Acta Univ. Sapientiae Math. 11(1), 87-98, (2019). https://doi.org/10.2478/ausm-2019-0008 DOI: https://doi.org/10.2478/ausm-2019-0008
Keogh, F. R. and Merkes, E. P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20, 8-12, (1969). https://doi.org/10.1090/S0002-9939-1969-0232926-9 DOI: https://doi.org/10.1090/S0002-9939-1969-0232926-9
Ma, W. C. and Minda, D., A unified treatment of some special classes of univalent functions, in Proceedings of the Conference on Complex Analysis (Tianjin), 157-169, Conf. Proc (1992). Lecture Notes Anal., I Int. Press, Cambridge, MA.
Maharana, S., Bansal, D. and Prajapat, J., Coefficient bounds for inverse of certain univalent functions, Bull. Math. Anal. Appl. 8(3), 59-65, (2016).
Mishra, A. K., Prajapat, J. and Maharana, S., Bounds on Hankel determinant for starlike and convex functions with respect to symmetric points, Cogent Math. 3, 1160557, (2016). https://doi.org/10.1080/23311835.2016.1160557 DOI: https://doi.org/10.1080/23311835.2016.1160557
Parihar, H. S., Agarwal, R. and Paliwal, G. S., Families of multivalent analytic functions associated with the convolution structure, Journal of Progressive Research in Mathematics, 6(1), 741-745, (2015).
Ponnusamy, S. and Ronning, F., Integral transforms of a class of analytic functions Complex Var. Elliptic Equ., 53(5), 423-434, (2008). https://doi.org/10.1080/17476930701685767 DOI: https://doi.org/10.1080/17476930701685767
Salagean, G. S., Subclasses of univalent functions, Lecture Notes in Math. (Springer-Verlag ) 1013, 362-372, (1983). https://doi.org/10.1007/BFb0066543 DOI: https://doi.org/10.1007/BFb0066543
Selvaraj, C. and Karthikeyan, K. R., Subclasses of analytic functions involving a certain family of linear operators, Internat. J. Contemp. Math. Sci. 3(13), 615-627, (2008).
Srivastava, H. M. and Attiya, A. A., An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integral Transforms Spec. Funct. 18, 207-216, (2007). https://doi.org/10.1080/10652460701208577 DOI: https://doi.org/10.1080/10652460701208577
Swaminathan, A., Certain sufficiency conditions on Gaussian hypergeometric functions J. Inequal. Pure Appl. Math. 5(4), 1-10, (2004).
Swaminathan, A., Sufficient conditions for hypergeometric functions to be in a certain class of analytic functions, Comp. Math. Appl. 59(4), 1578-1583, (2010). https://doi.org/10.1016/j.camwa.2009.12.029 DOI: https://doi.org/10.1016/j.camwa.2009.12.029
Wang, X. Y. and Wang, Z. R., Coefficient Inequality for a new subclass of analytic and univalent functions related to sigmoid function, Int. J. Mod. Math. Sci. 16(1), 51-57, (2018).
Wieclaw, K. T., Zaprawa, P., Gregorczyk, M. and Rysak, A., On the fekete-szego type functionals for close-to-convex functions Symmetry, doi:10.3390/sym11121497, 11, 1497, 1-17, (2019). https://doi.org/10.3390/sym11121497 DOI: https://doi.org/10.3390/sym11121497
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
