Ebrahim A. Adegani, Samaneh G. Hamidi, Jay M. Jahangiri, Ahmad Zireh

Coeﬃcient estimates for m-fold symmetric bi-subordinate functions

A function is said to be bi-univalent in the open unit disk U if both the function and its inverse map are univalent in U. By the same token, a function is said to be bisubordinate in U if both the function and its inverse map are subordinate to a given function in U. In this paper, we consider the m-fold symmtric transform of such functions and use their Faber polynomial expansions to ﬁnd upper bounds for their n-th (n ≥ 3) coeﬃcients subject to a given gap series condition. We also determine bounds for the ﬁrst two coeﬃcients of such functions with no restrictions imposed.

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