In this paper, we intorduce a family of analytic functions in the open unit disk which is bi-univalent. By the virtue of the Faber polynomial expansions, the estimation of n−th(n≥3) Taylor–Maclaurin coefficients an is obtained. Furthermore, the bounds value of the first two coefficients of such functions is established.
<abstract><p>The notion of a fuzzy subset is used to introduce certain subclasses of analytic functions. Mainly, this article presents several inclusion results and integral preserving properties. Also, certain applications of the analytic functions in terms of fuzzy structure will be discussed.</p></abstract>
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