Applications of extremal theorem and radius equation for a class of analytic functions
-
Liangpeng Xiong
and
Xiaoli Liu
Abstract
A linear operator D𝒫kf(z) : S → S is introduced, where S denotes the class of univalent analytic functions in open unit disk and 𝒫k is an arbitrary monotonically increasing function in k. We study a new class 𝒯𝒫k(α1, α2, α3, β) of analytic functions related to D𝒫kf(z). The main object of this paper is to give the radius equation between the class 𝒯𝒫k(α1, α2, α3,β) and the close-to-convex class of order α (0 ≤ α < 1). Also, we apply the extremal theorem to maximize |f(𝒳)(z)| over 𝒯𝒫k(α1, α2, α3, β), where 𝒳 = {0, 1, 2, …, k}, all the results are sharp.
Funding statement: This work was supported by Scientific Research Fund of SiChuan Provincial Education Department of China, Grant No.14ZB0364
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Articles in the same Issue
- A triple representation of lattice effect algebras
- Periods of morgan-voyce sequences and elliptic curves
- Multiplicative generalized derivations on ideals in semiprime rings
- A few remarks on Poincaré-Perron solutions and regularly varying solutions
- Applications of extremal theorem and radius equation for a class of analytic functions
- On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions
- New criteria for global exponential stability of linear time-varying volterra difference equations
- On approximation of functions by some hump matrix means of Fourier series
- Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
- Poisson kernels on semi-direct products of abelian groups
- Locally convex projective limit cones
- On the properties (wL) and (wV)
- On the existence of solutions for quadratic integral equations in Orlicz spaces
- Existence and uniqueness of best proximity points under rational contractivity conditions
- Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds
- On the internal approach to differential equations 3. Infinitesimal symmetries
- A Characterization of the discontinuity point set of strongly separately continuous functions on products
- Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators
- Multivariate EIV models
- On codes over 𝓡k, m and constructions for new binary self-dual codes
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