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MSC 2010: 30C45, 30C55One of the most important questions in the study of the classes of such functions is related to bounds on the modulus of functions (growth) or modulus of the derivative (distortion). The aim of this paper is to give the growth and distortion theorems for the close-to-convex harmonic functions in the open unit disc D.

Some Hölder-logarithmic estimates on Hardy-Sobolev spaces

Imed Feki, Ameni Massoudi (2024)

Czechoslovak Mathematical Journal

We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces $H^{k, p} (G)$ , where $k \in ℕ^{*}$ , $1 \leq p \leq \infty$ and $G$ is either the open unit disk $𝔻$ or the annular domain $G_{s}$ , $0 < s < 1$ of the complex space $ℂ$ . More precisely, we study the behavior on the interior of $G$ of any function $f$ belonging to the unit ball of the Hardy-Sobolev spaces $H^{k, p} (G)$ from its behavior on any open connected subset $I$ of the boundary $\partial G$ of $G$ with respect to the $L^{1}$ -norm. Our results can be viewed as an improvement and generalization of those established...

Some homeomorphisms of the sphere conformal off a curve.

Bishop, Christopher J. (1994)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

Some inclusion relationships for certain subclasses of meromorphic functions associated with a family of integral operators.

Selvaraj, C., Karthikeyan, K.R. (2009)

Acta Mathematica Universitatis Comenianae. New Series

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Some estimates of the integral $\int_{0}^{2 π} Log | P (e^{i θ}) | {(2 π)}^{- 1} d θ$ .

Some Estimates of the Integral $i n t_{0}^{2 p i} e x t L o g, | p (e^{i h e t a}) | {(2 p i)}^{- 1}, d h e t a$

Some extensions of sufficient conditions for univalence of an integral operator on the classes $𝒯_{j}, 𝒯_{j, μ}$ and $𝒮_{j} (p)$ .

Some extremal problems for certain families of analytic functions I

Some Extremal Problems for Functions Univalent in an Annulus.

Some families of analytic functions with negative coefficients

Some families of $p$ -valent functions with negative coefficients.

Some generalized convolution properties associated with certain subclasses of analytic functions.

Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

Some Hölder-logarithmic estimates on Hardy-Sobolev spaces

Some homeomorphisms of the sphere conformal off a curve.

Some inclusion relationships for certain subclasses of meromorphic functions associated with a family of integral operators.

Some Inequaliteis for Starklike Functions.

Some inequalities associated with a linear operator defined for a class of analytic functions.

Some inequalities associated with a linear operator defined for a class of multivalent functions.

Some inequalities concerning starlike and convex function.

Some inequalities exhibiting certain properties of some subclasses of multivalently analytic functions.

Some Inequalities for Analytic Functions with a Finite Dirichlet Integral on the Unit Disc.

Some inequalities for convex, starlike, and close-to-convex mappings

Some inequalities for regular and univalent functions

Currently displaying 81 – 100 of 294