The purpose of the present paper is to investigate some integral preserving properties for certain analytic functions in the open unit disk. We also obtain the conditions for close-to-convex functions in a sector. Our results contain some interesting corollaries as the special cases.
Form preserving linear integral operators
โ Scribed by Tzon Tzer Lu; Sui Sun Cheng
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 893 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
โฆ Synopsis
This paper is concerned with integral operators which are defined by means of continuous kernel functions. We give necessary and sufficient conditions imposed on the kernels such that families of continuous functions with various distinctive forms are left invariant under the corresponding operators.
๐ SIMILAR VOLUMES
The minimal rank of a square matrix is studied, and the linear operators preserving it are characterized. Some related results are presented and some unsolved problems are discussed.
In this note we introduce a simple and efficient technique for studying the asymptotic behavior of the iterates of a large class of positive linear operators preserving constant functions.