Universally prestarlike functions associated with shell like domain

  • K. Vijaya Department of Mathematics School of Advanced Sciences Vellore Institute of Technoloy Vellore, India
  • G. Murugusundaramoorthy Department of Mathematics School of Advanced Sciences Vellore Institute of Technoloy Vellore, India
  • S. Yalçın Department of Mathematics Faculty of Arts and Science Bursa Uludag University Bursa, Turkey

Анотація

In this paper, we introduce universally prestarlike
generalized functions of order $\vartheta $ with $\vartheta \leq 1$ associated with shell like domain, and we get
coefficient bounds and the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for
such functions.

Біографії авторів

K. Vijaya, Department of Mathematics School of Advanced Sciences Vellore Institute of Technoloy Vellore, India

Department of Mathematics School of Advanced Sciences
Vellore Institute of Technoloy
Vellore, India

G. Murugusundaramoorthy, Department of Mathematics School of Advanced Sciences Vellore Institute of Technoloy Vellore, India

Department of Mathematics School of Advanced Sciences
Vellore Institute of Technoloy
Vellore, India

S. Yalçın, Department of Mathematics Faculty of Arts and Science Bursa Uludag University Bursa, Turkey

Department of Mathematics Faculty of Arts and Science
Bursa Uludag University
Bursa, Turkey

Посилання

O.P. Ahuja, M. Kasthuri, G. Murugusundaramoorthy, K. Vijaya, Upper bounds of second Hankel determinant for universally prestarlike functions, J. Korean Math. Soc., 55 (2018) №5, 1019–1030.

P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.

M. Fekete, G. Szeg¨o, Eine Bemerkung ¨uber ungerade schlichte Funktionen, J. London. Math. Soc., 8 (1933), 85–89.

U. Grenander, G. Szeg¨o, Toeplitz forms and their applications, Univ. of California Press, Berkeley and Los Angeles, 1958.

A. Janteng, S.A. Halim, M. Darus, Hankel determinant for starlike and convex functions, Int. J. Math. Anal, 1 (13-16) (2007), 619—625.

S.K. Lee, V. Ravichandaran, S.Superamanian, Bounds for the second Hankel determinant of certain univalent functions, J. Inequal. Appl., 281 (2013), 17 p.

R.J. Libera, E.J. Zlotkiewicz, Early coefficients of the inverse of a regular convex function, Proc. Amer. Math. Soc., 85 (1982), №2, 225—230.

M.S. Liu, J.F.g Xu, M. Yang, Upper bound of second Hankel determinant for certain subclasses of analytic functions, Abs. Appl. Anal., 2014, Article ID 603180, 10 p.

W.C. Ma, D. Minda, A unified treatment of some special classes of functions, In: Proceedings of the Conference on Complex Analysis, Tianjin, 1992, 157–169, Conf. Proc. Lecture Notes Anal. 1. Int. Press, Cambridge, MA, 1994.

J.W. Noonan, D.K. Thomas, On the second Hankel determinant of areally mean p−valent functions, Trans. Amer. Math. Soc., 223 (1976), №2, 337–346.

R.K. Raina, J. Sokol, On coeffcient estimates for a certain class of starlike functions, Hacettepe Journal of Math. and Stat., 44 (2015), №6, 1427–1433.

S. Ruscheweyh, Some properties of prestarlike and universally prestarlike functions, In: International Conf. Geometric Function Theory, J. Analysis., 15 (2007), 247–254.

S. Ruscheweyh, L. Salinas, Universally prestarlike functions as convolution multipliers, Mathematische Zeitschrift, (2009), 607–617.

S. Ruscheweyh, L. Salinas, T. Sugawa, Completely monotone sequences and universally prestarlike functions, Isreal J. Math., 171 (2009), 285–304.

S. Ruscheweyh, Convolutions in Geometric Function Theory, Sem. Math. Sup., V.83, Presses Univ. Montreal, 1982.

T.N. Shanmugam, J. Lourthu Mary, Properties of universally prestarlike functions, International Journal of Engineering Research and Technology, 1(10), (2012).

T.N. Shanmugam, J. Lourthu Mary, A note on universally prestarlike functions, Stud. Univ. Babes-Bolyai Math., 57 (2012), №1, 53–60.

T.N. Shanmugam, J. Lourthu Mary, Fekete-Szeg¨o inequality for Universally prestarlike functions, Fractional calculus and Applied analysis, 13 (2010), №14, 385–394.

B. Srutha Keerthi, M. Revathi, G. Murugusundaramoorthy, The second hankel determinant for certain classes of analytic univalent functions, Inter. J. Appl. Engg. Research, 9 (2014), №22, 12241–12254.

J. Sokol, D.K. Thomas, Further results on a class of starlike functions related to the Bernoulli lemniscate, Houston J. Math., 44 (2018), 83–95.

Опубліковано
2022-03-31
Як цитувати
Vijaya, K., Murugusundaramoorthy, G., & Yalçın, S. (2022). Universally prestarlike functions associated with shell like domain. Математичні студії, 57(1), 53-61. https://doi.org/10.30970/ms.57.1.53-61
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