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Application of Chebyshev polynomials to classes of analytic functions.
- Source :
-
Comptes Rendus. Mathématique . May2015, Vol. 353 Issue 5, p433-438. 6p. - Publication Year :
- 2015
-
Abstract
- Our objective in this paper is to consider some basic properties of the familiar Chebyshev polynomials in the theory of analytic functions. We investigate some basic useful characteristics for a class H ( t ) , t ∈ ( 1 / 2 , 1 ] , of functions f , with f ( 0 ) = 0 , f ′ ( 0 ) = 1 , analytic in the open unit disc U = { z : | z | < 1 } satisfying the condition that 1 + z f ″ ( z ) f ′ ( z ) ≺ H ( z , t ) = 1 1 − 2 t z + z 2 ( z ∈ U ) , where H ( z , t ) is the generating function of the second kind of Chebyshev polynomials. The Fekete–Szegö problem in the class is also solved. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1631073X
- Volume :
- 353
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Comptes Rendus. Mathématique
- Publication Type :
- Academic Journal
- Accession number :
- 102074994
- Full Text :
- https://doi.org/10.1016/j.crma.2015.02.001