Coefficient Estimate of bi-Bazilevič Functions Associated with Fractional q-calculus Operators

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Murugusundaramoorthy, G.^a | Janani, T.^b | Purohit, Sunil Dutt^{c; *}

Affiliations: [a] School of Advanced Sciences, VIT University, Vellore-632014, Tamilnadu, India. gmsmoorthy@yahoo.com | [b] School of Computer Sciences & Engineering, VIT University, Vellore-632014, Tamilnadu, India. tjanani1985@gmail.com | [c] Department of HEAS (Mathematics), Rajasthan Technical University, Kota-324010, Rajasthan, India. sunil_a_purohit@yahoo.com

Correspondence: [*] Address for correspondence: Department of HEAS (Mathematics), Rajasthan Technical University, Kota-324010, Rajasthan, India

Abstract: In this paper, we introduce and investigate two new subclasses of the function class ∑ of bi-univalent functions defined in the open unit disk, which are associated with fractional q-calculus operators, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

Keywords: Analytic functions, Univalent functions, Bi-univalent functions, Bi-starlike and biconvex functions, Bi-Bazilevič functions, Fractional q-calculus operators

DOI: 10.3233/FI-2017-1478

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 49-62, 2017