Further Geometric Properties of a Subclass of Univalent Functions
DOI:
https://doi.org/10.14419/ijams.v7i1.30610Published:
2020-05-18Keywords:
Analytic Functions, Univalent Functions, Differential Operator, Neighborhood.Abstract
This present paper aims to investigate further, certain characterization properties for a subclass of univalent function defined by a generalized differential operator. In particular, necessary and sufficient conditions for the function to belong to the subclass is established. Additionally, we provide the ð›…-neighborhood properties for the function by making use of the necessary and sufficient conditions. The results obtained are new geometric properties for the subclass
References
[1] Duren P.L., Univalent functions, A Series of Comprehensive studies in Mathematics by Springer-Verlag, New York Berlin-Heidelberg-Tokyo, 259 (1983).
[2] Pommerenke C, Univalent functions with a chapter on quadratic differentials by Gerr Jesen,vandenhoeck and Ruprecht in Gottingen, Germany (1975)
[3] Bieberbach L. ber die Koeffizienten derjenigen Potenzreihen, welcheeine Schlichting Abbildung des Einheitskreises vermitteln, Preuss, Akad. Wiss., Phys. Math. K1. (1916) 138:940-955.
[4] Goodman A.W., Univalent functions, Mariner Publ. comp., Tampa, Florida, (1983).
[5] Mocanu P.T, Bulboacă T, Sãlãgean GŞ. Teoria Geometrică a Funcţiilor Analitice, Casa Cărtii de Ştiinţă, Cluj-Napoca, (1999), 77-81.
[6] Robertson MS. “On the theory of univalent functionsâ€. Ann. Math. (1936) 37:374-408. https://doi.org/10.2307/1968451.
[7] Sãlãgean G. Ş. Subclasses of univalent functions. Complex Analysis 5th Romanian-Finish Seminar, Part I (Bucharest, 1981), Lecture Notes Math.1031. Springer-Verlag. 1981 362-372. https://doi.org/10.1007/BFb0066543.
[8] Raducanu, D. “On a subclass of univalent functions defined by a generalized differential operatorâ€. Math. Reports 13, 63 no. 2 (2011), 197-203
[9] Opoola O. T., “On a subclass of univalent function defined by a Generalized Differential Operatorâ€, International journal of mathematical Analysis, 11 no. 18 (2017), 869-876. https://doi.org/10.12988/ijma.2017.7232.
[10] Oyekan, E. A. “Some properties for a subclass of univalent functionsâ€, Asian journal of mathematics and computer research, 20 no. 1 (2017), 32- 37. http://www.ikprress.org/index.php/AJOMCOR/article/view/981
[11] Ruscheweyh S., New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109-115. https://doi.org/10.1090/S0002-9939-1975-0367176-1.
[12] Oyekan, E. A. and Kehinde R. Subordination results on certain new subclasses of analytic functions, “Confluence Journal of Pure and Applied Sciences†(CJPAS), 2 no. 2(2018), 116-123.
[13] Goodman, A. W. Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., 8(1957) 598–601. https://doi.org/10.1090/S0002-9939-1957-0086879-9.
[14] Ruscheweyh, S. Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 81 (1981) 521–527. https://doi.org/10.1090/S0002-9939-1981-0601721-6.
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