论文标题
广义高几年功能的几何特性
Geometric Properties of Generalized Hypergeometric Functions
论文作者
论文摘要
在本文中，使用$ _4f_3 \使用Hadamard产品（^{a_1，\，\，a_2，a_2，\，\，a_3，\，\，\，\，A_4} _ {b_1，\，\，\，b_2，\，\，\，\，b_3}; z \ right） $ \ MATHCAL {i}^{a_1，a_2，a_3，a_4} _ {b_1，b_2，b_3}（f）（z）（z）$。 $ _4F_3 \ left的几何属性（^{a_1，\，\，a_2，\，\，a_3，\，\，a_4} _ {b_1，\，\，\，\，\，\，\，b_3}; z \ z \ right）$超细计）$超数字函数是针对统一函数的各种子类函数的。另外，我们考虑一个运算符$ \ Mathcal {i}^{a，\ frac {b} {4}，\ frac {b+1} {4} {4}，\ frac {b+2} {4} {4} {4} {4}，\ frac {b+3} \ frac {c+1} {4}，\ frac {c+2} {4}，\ frac {c+3} {4}}} {4}}}}（f）（z）$$ = z \，， _5f_4 \ left（^{a，\ frac {b} {4}，\ frac {b+1} {4} {4}，\ frac {b+2} {4} {4}，\ frac {b+3} \ frac {c+2} {4}，\ frac {c+3} {4}};在主要结果中，在$ a，b，$ $ c $上确定条件，以使功能$ z \， _5f_4 \ left（^{a，\ frac {b} {4}，\ frac {b+1} {4} {4}，\ frac {b+2} {4} {4}，\ frac {b+3} \ frac {C+2} {4}，\ frac {c+3} {4}};随后，对$ a，\，b，\，c，c，\，$和$β$的条件是使用积分运算符确定的，使得属于$ \ nathcal {r}（β）$和$ \ nathcal {s} $的函数映射到$ \ nmatcal $ \ nmatcal {s} $ { $ ucv $和$ \ nathcal {s} _p $。
In this article, Using Hadamard product for $_4F_3\left(^{a_1,\, a_2,\, a_3,\, a_4}_{b_1,\, b_2,\, b_3};z\right)$ hypergeometric function with normalized analytic functions in the open unit disc, an operator $\mathcal{I}^{a_1,a_2,a_3,a_4}_{b_1,b_2,b_3}(f)(z)$ is introduced. Geometric properties of $_4F_3\left(^{a_1,\, a_2,\, a_3,\, a_4}_{b_1,\, b_2,\, b_3};z\right)$ hypergeometric functions are discussed for various subclasses of univalent functions. Also, we consider an operator $\mathcal{I}^{ a,\frac{b}{4},\frac{b+1}{4},\frac{b+2}{4},\frac{b+3}{4} }_{ \frac{c}{4}, \frac{c+1}{4}, \frac{c+2}{4},\frac{c+3}{4} }(f)(z)$$= z\, _5F_4\left(^{a,\frac{b}{4},\frac{b+1}{4},\frac{b+2}{4},\frac{b+3}{4}}_{\frac{c}{4}, \frac{c+1}{4}, \frac{c+2}{4},\frac{c+3}{4}}; z\right)*f(z)$, where, $_5F_4(z)$ hypergeometric function and the $*$ is usual Hadamard product. In the main results, conditions are determined on $ a,b,$ and $c$ such that the function $z\, _5F_4\left(^{a,\frac{b}{4},\frac{b+1}{4},\frac{b+2}{4},\frac{b+3}{4}}_{\frac{c}{4}, \frac{c+1}{4}, \frac{c+2}{4},\frac{c+3}{4}}; z\right)$ is in the each of the classes $ \mathcal{S}^{*}_λ $, $ \mathcal{C}_λ$, $UCV$ and $\mathcal{S}_p$. Subsequently, conditions on $a,\,b,\,c,\, λ,$ and $β$ are determined using the integral operator such that functions belonging to $\mathcal{R}(β)$ and $\mathcal{S}$ are mapped onto each of the classes $\mathcal{S}^*_λ$, $\mathcal{C}_λ$, $UCV$, and $\mathcal{S}_p$.
