# Sharp coefficient inequalities for a class of analytic functions defined by q-difference operator associated with q-Lemniscate of Bernoulli

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## Keywords:

Analytic functions, q-Differential operator, Hankel determinant, q-Starlike functions, Ruscheweyh q-differential operator, q-Lemniscate of Bernoulli## Abstract

Quantum theory has many applications in mathematics, particularly in the study of special functions and quantum physics. In this article, based on the concept of Lemniscate of Bernoulli, we provide q-Lemniscate of Bernoulli (x2 +y2) -2(x2 - y2) = q2 - 1. The q-Lemniscate Bernoulli is used to define a new class of analytic functions using a quantum di¤erence operator, and for this class,

an upper bound Fekete-Szegö problems and the second Hankel determinant are studied. Furthermore, several known cases with proven findings are presented. In addition, by using the Ruscheweyh q-di¤erential operator, certain useful applications of the main findings are attained.

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