Abstract
The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients |am+1| and |a2m+1| are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.
Highlights
Introduction and Preliminary ResultsCoefficient Estimates and theThe study of bi-univalent functions has its origins in a 1967 paper published byLewin [1], where he introduced and first investigated the class of bi-univalent functions
Of the paper, the original results obtained by the authors are presented in three definitions of new subclasses of bi-univalent functions and theorems concerning coefficient estimates and Fekete–Szegő functional for the newly defined classes defined by ( p, q)-derivative operator given in relations (5)–(7)
Following the line of research initiated by Srivastava et al [20], three new classes of m-fold bi-univalent functions are introduced in Definitions 3–5
Summary
Introduction and Preliminary ResultsCoefficient Estimates and theThe study of bi-univalent functions has its origins in a 1967 paper published byLewin [1], where he introduced and first investigated the class of bi-univalent functions. The subclass S ⊂ A is formed of functions in class A which are univalent in U. Let Σ denote the class of all bi-univalent functions in U given by (1).
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