An operator I is said to be an averaging (or mean-value) operator on a set $${\mathcal {K}}$$ K of analytic functions in $$\Delta =\{z: |z|<1\}$$ Δ = { z : | z | < 1 } , if $$I[f](0)=f(0)$$ I [ f ] ( 0 ) = f ( 0 ) and $$I[f](\Delta )$$ I [ f ] ( Δ ) is contained in the convex hull of $$f(\Delta )$$ f ( Δ ) for all $$f\in {\mathcal {K}}$$ f ∈ K . In this work we consider the class $$\mathcal {SP}(\alpha )$$ SP ( α ) 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.
Analysis and Mathematical Physics – Springer Journals
Published: Dec 23, 2019
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.