Some properties of a new subclass of analytic univalent functions defined by multiplier transformation
DOI:
https://doi.org/10.24193/subbmath.2019.1.08Keywords:
Analytic, Univalent functions, Multiplier Transformation.Abstract
The purpose of the present paper is to study the integral operator of the form ∫z0{Inμf(t)t}δdt where $f$ belongs to the subclass $C(n,\alpha,\beta, \mu)$ and $\delta$ is a real number. We obtain integral characterization for the subclass $C(n,\alpha,\beta, \mu)$ and also prove distortion, rotation and radii theorem for this class. Relevant connections of the results presented here with various known results are briefly indicated.
Mathematics Subject Classification (2010): 30C45, 30C50, 30C55.
References
Cho, N.E., Kim, T.H., Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc., 40(2003), no. 3, 399-410.
Cho, N.E., Srivastava, H.M., Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modell., 37(2003), no. 1-2, 39-49.
Goodman, A.W., Univalent Functions, Vol. I and II, Mariner Publishing Company, Florida, 1983.
Kadioˇglu, E., On subclass of univalent functions with negative coefficients, Appl. Math. Comput., 146(2003), 351-358.
Kaplan, W., Close-to-Convex Schlicht functions, Mich. Math. J., 1(1952), 169-185.
Kim, Y.J., Univalence of Certain Integrals, Ph.D. Thesis, University of Cincinnati, 1972. [7] MacGregor, T.H., Univalent power series whose coefficients have monotonic properties, Math. Z., 112(1969), 222-228.
Merkes, E.P., Wright, D.J., On the univalence of certain integrals, Proc. Amer. Math. Soc., 27(1971), 97-100.
Mishra, R.S., Geometrical and Analytical Properties of Certain Classes Related to Univalent Functions, Ph.D. Thesis, C.S.J.M. University, Kanpur, India, 2007.
Nunokawa, M., On the univalence of certain integral, Proc. Japan Acad., 45(1969), 841- 845.
Nunokawa, M., On the univalence of certain integral, Trans. Amer. Math. Soc., 146(1969), 439-440.
Patil, D.A., Thakare, N.K., On univalence of certain integral, Indian J. Pure Appl. Math., 11 (1980), 1626-1642.
Pfaltzgraff, J.A., Univalence of the integral of f t(z)λ, Bull. Lon. Math. Soc., 7(1975), 254-256.
Pinchuk, B., On starlike and convex functions of order α, Duke Math. J., 35(1968), 721-734.
Porwal, S., Mapping properties of an integral operator, Acta Univ. Apul., 27(2011), 151- 155.
Reade, M.O., On close-to-convex univalent functions, Mich. Math. J., 3(1955-56), 59-62. [17] Robertson, M.S., On the theory of univalent functions, Ann. Math., 37(1936), 374-408. [18] Royster, W.C., On the univalence of certain integral, Mich. Math. J., 12(1965), 385-387. [19] S˘al˘agean, G.S., Subclasses of univalent functions, Complex Analysis-Fifth Romanian Finish Seminar, Bucharest, 1(1983), 362-372.
Shukla, S.L., Kumar, V., Remarks on a paper of Patil and Thakare, Indian J. Pure Appl. Math., 13(1982), 1513-1525.
Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51(1975), 109-116.
Uralegaddi, B.A., Somanatha, C., Certain Classes of Univalent Functions, in Current Topics in Analytic Function Theory, 371-374, World Sci. Publishing, River Edge, NJ.
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