In the current paper, we study a majorization issue for a general category S * ( ϑ ) of starlike functions, the region of which is often symmetric with respect to the real axis. For various special symmetric functions ϑ , corresponding consequences of the main result are also presented with some relevant connections of the outcomes rendered here with those obtained in recent research. Moreover, coefficient bounds for some majorized functions are estimated.
Abstract. Let g υ (z) be the classical Bessel function of the first kind of order υ and f be an analytic function defined on the unit disc ∆. Suppose the operator H ( f ) be defined. In this paper we identify subfamily M n (α, β) of univalent functions and obtain conditions on the parameter υ such that f ∈ M n (α, β) implies H ( f ) ∈ M n (α, β).
Let $g_{\upsilon}(z)$ be the classical Bessel function of the first kind of order $\upsilon$ and $f$ be an analytic function defined on the unit disc $\Delta$. Suppose the operator $H(f)$ be defined by $H(f)(z)=\frac{z}{\frac{z}{f(z)}*\frac{g_{\upsilon}(z)}{z}}$. In this paper we identify subfamily $M_{n}(\alpha,\beta)$ of univalent functions and obtain conditions on the parameter $\upsilon$ such that $f\in M_{n}(\alpha,\beta)$ implies $H(f)\in M_{n}(\alpha,\beta)$.
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