Logarithmic coefficients for starlike and convex functions of complex order defined by subordination

Downloads

Abstract

The aim of this paper is to find the bounds for the logarithmic coefficients $\gamma_n$ of the general classes of starlike and convex functions of complex order, $S_d^*(\Psi)$ and $K_d(\Psi)$ respectively. Our results would generalize some of the previous paper like [1] E. A. Adegani et al., [3] Ali et al.,etc.

Keywords:

Starlike function and convex function of Complex order, subordination, logarithmic coefficients

Mathematics Subject Classification:

Mathematics
  • Neetu Shekhawat Department of Mathematics, AMITY School of Applied Science, AMITY University Rajasthan, Jaipur-302002 , India.
  • Ravi Shanker Dubey Department of Mathematics, AMITY School of Applied Science, AMITY University Rajasthan, Jaipur-302002 , India.
  • Pages: 665-669
  • Date Published: 01-01-2021
  • Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

[I] Adegani E.A., Cho N.E. and Jafari M., Logarithmic Coefficients for Univalent Functions Defined by Subordination, Mathematics 2019, 7,408;doi: 10.3390

KayumovI.R., On Brennan's conjecture for a special class of functions.Math.Notes2005,78,498-502. [CrossRef].

Ali M.F., Vasudevarao A., On logarithmic coefficients of some close-to-convex functions. Proc. Am. Math. Soc. 2018, 146, 1131-1142.

Nasr M_A. and Aouf M.K., Mansoura Sci. Bull Egypt, $1982,9,565-82$.

Ma W.C.,Minda D. A.,Unified treatment of some special classes of univalent functions. In Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Intemat Press: Cambridge, MA, USA, 1992, 157-169.

DurenP.L. ,Univalent Functions; Springer: New York, NY, USA; Berlin/Heidelberg, Germany; Tokyo, Japan, 1983.

Kumar U.P.,Vasudevarao A., Logarithmic coefficients for certain subclasses of close-to-convex functions. Monatsh. Math. 2018, 187, 543-563.

[$l Nehari $Z$, Conformal Mapping: McGraw-Hill: New York, NY, USA, 1952.

Ruscheweyh S.,Stankiewicz J., Subordination under convex univalent function. Bull. Pol. Acad. Sci. Math. 1985, 33, 499-502.

Rogosinski W., On the coefficients of subordinate functions. Proc. Lond. Math. Soc. 1943, 48, 48-82.

Prokhorov D.V.,Szynal J., Inverse coefficients for $(alpha ; beta)$ convex functions. Ann. Univ. Mariae Curie-Sklodowska Sect. A 1984, 35, 125-143.

Ruscheweyh S., New criteria for univalent functions. Proc. Am. Math. Soc. 1975, 49, 109-115.

RuscheweyhS_, Sheil-Small, T. Hadamard product of schlicht functions and the Poyla Schoenberg conjecture. Comment. Math. Helv. 1973, 48, 119-135

Ponnusamy S., Sharma N.L. Wirths K.J., Logarithmic Coefficients of the Inverse of Univalent Functions. Results Math. 2018, 73, 160 .

Metrics

Metrics Loading ...

Published

01-01-2021

How to Cite

Neetu Shekhawat, and Ravi Shanker Dubey. “Logarithmic Coefficients for Starlike and Convex Functions of Complex Order Defined by Subordination”. Malaya Journal of Matematik, vol. 9, no. 01, Jan. 2021, pp. 665-9, https://www.malayajournal.org/index.php/mjm/article/view/1108.