Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, Tehran, Iran.

Abstract

In the present investigation, our main aim is to introduce a certain subclass of analytic univalent functions related to the Error function. We discuss the implications of our main results, including the coefficient bound, extreme points, weighted mean, convolution, convexity, and radii properties,  as well as any other related properties.

Keywords

[1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical functions with formulas, Graphs and Matematical Tables, Dorer Publications Inc., New York, 1965.
[2] S. Altınkaya and S.O. Olatunji, Generalized distribution for analytic function classes associated with error functions and Bell numbers, Bol. Soc. Mat. Mex., 26 (2020), pp. 377–384. 
[3] H. Alzer, Error functions inequalities, Adv. Comput. Math., 33 (2010), pp. 349-379.
[4] L. Carlitz, The inverse of the error function, Pacific J. Math., 33 (1963), pp. 459-470.
[5] D. Coman, The radius of starlikeness for error function, Stud. Univ. Babes Bolyal Math., 36 (1991), pp. 13-16.
[6] P.L. Duren, Univalent functions, Grundelheren der Mathematischen Wissenchaften 259 Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
[7] A. Elbert and A. Laforgia, The zeros of the complementary error function, Numer. Algorithms., 49 (2008), pp. 153-157.
[8] J.M. Jahangiri, C. Ramachandran and S. Annamalai, Fekete-Szegö problem for certain analytic functions defined by hypergeometric functions and Jacobi polynomial, J. Fract. Calc. Appl., 9 (2018), pp. 1–7.
[9] S.N. Malik, S. Riaz, M. Raza, and S. Zainab, Fekete-Szeg\"o Problem of Functions Associated with Hyperbolic Domains, Sahand Commun. Math. Anal., 14 (2019), pp.73-88.
[10] Sh. Najafzadeh, Some results on univalent holomorphic functions based on q-analogue of Noor operator, Int. J. Appl. Math., 32(5) (2019), pp. 775-784.
[11] Z. Orouji and A. Ebadian, Integral Operators on the Besov Spaces and Subclasses of Univalent Functions, Sahand Commun. Math. Anal., 17(4) (2020), pp.61-69.
[12] C. Ramachandran, L. Vanitha and S. Kanas, Certain results on q-starlike and q-convex error functions, Math. Slovaca., 68 (2018), pp. 361-368.