In the proposed work, we introduce a new subclass of univalent analytic functions denoted by \(\mathcal {S}^{*}_{ChE}\) defined in the open unit disk \(\mathbb { D}\) with the help of subordination involving the quotient of the analytic representation of the cosine hyperbolic and exponential functions. For this function class, we determine sharp upper bounds of some of the initial coefficients, Fekete–Szegö functional and some sharp estimates of the Hankel determinant of different orders. Further, some sharp bounds of inverse and logarithmic coefficients, Zalcman and Krushkal inequalities are obtained for such a family. Our approach is based on the fact that the coefficients of functions in such a family and coefficients of corresponding Schwarz functions are interrelated. If we adopt this approach, exact estimate of the functional may easily be obtained. Furthermore, bounds for two-fold and three-fold symmetric functions belonging to said class are obtained.
