A Class of Nonlinear Averaging Integral Operators |
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| Institution: | 1. Department of Mathematics, State University of New York, Brockport, New York, 14420;2. Faculty of Mathematics, Babes-Bolyai University, 3400 Cluj, Napoca, Romania |
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| Abstract: | LetHbe the class of analytic functions defined in the unit discU, and let coEdenote the convex hull of a setEinC. IfK⊂H, then an operatorI:K→His an averaging operator ifIf](0) =f(0) andIf](U) ⊂ cof(U), for allf∈K. The authors show that the operatorIβ,γf](z) ≡ γz−γ∫z0fβ(t)tγ−1dt]1/βis an averaging operator on certain subsets ofH. |
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