An operator I is said to be an averaging (or mean-value) operator on a set \({\mathcal {K}}\) of analytic functions in \(\Delta =\{z: |z|<1\}\), if \(I[f](0)=f(0)\) and \(I[f](\Delta )\) is contained in the convex hull of \(f(\Delta )\) for all \(f\in {\mathcal {K}}\). In this work we consider the class \(\mathcal {SP}(\alpha )\) of functions defined by us (Folia Sci Univ Technol Resov 28:35–42, 1993), which is connected with the class of uniformly convex functions introduced by Goodman (Ann Polon Math 56:87–92, 1991). We describe an interesting new construction of averaging operators which might attract a considerable attention of mathematicians working in the field.

中文翻译：

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平均算子和与抛物线有关的星形函数的类

运算符I据说是\（\ Delta = \ {z：| z | <1 \}中的一组解析函数\（{\ mathcal {K}} \）的平均（或均值）运算符\） ，如果\（I [F]（0）= F（0）\）和\（I [F]（\德尔塔）\）的含量在所述凸包\（F（\德尔塔）\）为全部\（f \ in {\ mathcal {K}} \）。在这项工作中，我们考虑类\（\ mathcal {SP}（\ alpha）\）我们定义的函数（Folia Sci Univ Technol Resov 28：35–42，1993），与Goodman引入的一类均匀凸函数有关（Ann Polon Math 56：87–92，1991）。我们描述了一个有趣的平均算子的新结构，它可能会吸引在该领域工作的数学家的相当大的关注。