COEFFICIENT ESTIMATES FOR SUBCLASSES OF BI-UNIVALENT FUNCTIONS WITH PASCAL OPERATOR | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 15, Issue 1, January 2024, Pages 1-9 PDF (332.43 K) | ||
| Document Type: Reviews | ||
| DOI: 10.21608/jfca.2024.221079.1021 | ||
| Author | ||
| G Thirupathi* | ||
| Department of Mathematics, Ayya Nadar Janaki Ammal College, Sivakasi -626 124 | ||
| Abstract | ||
| In the present paper, we introduce two new subclasses of the function class of bi-univalent functions defi ned in the open unit disc U . We find the bounds on the initial coefficients c2 and c3 and upper bounds for the Fekete-Szego functional for the functions in this class.Motivated by the work of H. M. Srivastava et al. construct a new subclass of biunivalent functions governed by the Pascal distribution series. Then, we investigate the optimal bounds for the Taylor - Maclaurin coefficients c2 and c3 in our new subclass. In Communications and Engineering elds the Pascal distribution has been widely used (see [11]). Recently, in geometric function theory, there has been a growing interest in studying the geometric properties of analytic functions associated with the Pascal distribution. This distribution is based on the binomial theorem with a negative exponent and it describes the probability of m success and n failure in (n + m-1) trials, and success on (n + m)th trials where (1- q) is the probability of success. | ||
| Keywords | ||
| analytic functions; bi-univalent functions; starlike and convex functions; coefficient bounds; Pascal operator | ||
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