Approximation of analytic functions by an absolutely convergent Dirichlet series
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DOI: 10.1007/s00013-021-01616-x
Abstract: In the paper, an absolutely convergent Dirichlet series whose shifts approximate a wide class of analytic functions is constructed. This series is close in the mean to the Riemann zeta-function. read more here.
Keywords: convergent dirichlet; dirichlet series; analytic functions; absolutely convergent ... See more keywords
Unified Approach to Starlike and Convex Functions Involving Convolution Between Analytic Functions
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DOI: 10.1007/s00025-018-0782-0
Abstract: Using the idea of convolution between analytic functions, we define a class $$\mathcal {UM}(g,\gamma ,b,k)$$UM(g,γ,b,k) of analytic functions comprising of starlike and convex functions. These functions map the open unit disc on to the conic… read more here.
Keywords: convolution analytic; starlike convex; analytic functions; convex functions ... See more keywords
Co-Isometric Weighted Composition Operators on Hilbert Spaces of Analytic Functions
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DOI: 10.1007/s00025-020-01253-w
Abstract: We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural… read more here.
Keywords: weighted composition; analytic functions; isometric weighted; operators hilbert ... See more keywords
Approximation of Certain Non-vanishing Analytic Functions in a Parabolic Region
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DOI: 10.1007/s00025-021-01434-1
Abstract: In this work, we consider a class of analytic functions f defined in the unit disk for which the values of $$zf'/f$$ lie in a parabolic region of the right-half plane. By using a well-known… read more here.
Keywords: vanishing analytic; analytic functions; approximation certain; parabolic region ... See more keywords
Residues and Argument Principle for A(z)-Analytic Functions
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DOI: 10.1007/s10958-020-04696-2
Abstract: In this paper, we obtain formulas for residues and prove analogs of the argument principle and Rouche theorems for A(z)-analytic functions. read more here.
Keywords: principle analytic; argument principle; analytic functions; residues argument ... See more keywords
Outer Functions in Classes of Analytic Functions of Variable Smoothness
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DOI: 10.1007/s10958-020-05091-7
Abstract: We use a Holder condition with respect to a variable exponent Lebesgue norm to introduce classes of analytic functions in a disc and of holomorphic functions in a ball. We describe outer functions in the… read more here.
Keywords: analytic functions; variable smoothness; functions classes; functions variable ... See more keywords
Bohr Inequalities in Some Classes of Analytic Functions
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DOI: 10.1007/s10958-020-05165-6
Abstract: The paper is a review of the latest results of I. R. Kayumov and S. Ponnusamy on the Bohr inequality. An exact estimate in the strong Bohr inequality is obtained and the Bohr–Rogosinski radius for… read more here.
Keywords: inequalities classes; bohr inequalities; classes analytic; analytic functions ... See more keywords
Radius Problems for Some Subclasses of Analytic Functions
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DOI: 10.1007/s11785-016-0584-x
Abstract: In this work, we define the class $${\mathcal {M}}(\alpha )$$M(α) of normalized analytic functions which satisfy the following two-sided inequality: $$\begin{aligned} 1+\frac{\alpha -\pi }{2\sin \alpha }< {{\mathfrak {R}}}{{\mathfrak {e}}}\left\{ \frac{zf'(z)}{f(z)}\right\} read more here.
Keywords: analytic functions; radius problems; problems subclasses; subclasses analytic ... See more keywords
Riemann–Hilbert Problems for Hardy Space of Meta-Analytic Functions on the Unit Disc
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DOI: 10.1007/s11785-017-0705-1
Abstract: The aim of this paper is to study Riemann–Hilbert problems for Hardy space of a class of meta-analytic functions defined on the unit disc. Here, the meta-analytic functions we focus on are null-solutions to a… read more here.
Keywords: hardy space; meta analytic; unit disc; analytic functions ... See more keywords
Subclass of analytic functions associated with Poisson distribution series
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DOI: 10.1007/s13370-020-00788-z
Abstract: In this paper, we find the necessary and sufficient conditions, inclusion relations for Poisson distribution series $${\mathcal {K}}(m,z)=z+\sum \nolimits _{n=2}^{\infty }\frac{m^{n-1}}{(n-1)!}e^{-m}z^{n}$$ belonging to a subclass $$\mathcal {TS}(\lambda ,\alpha ,\beta )$$ of analytic functions with negative… read more here.
Keywords: distribution series; subclass; poisson distribution; analytic functions ... See more keywords
Bohr Inequality for Odd Analytic Functions
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DOI: 10.1007/s40315-017-0206-2
Abstract: We determine the Bohr radius for the class of odd functions f satisfying $$|f(z)|\le 1$$|f(z)|≤1 for all $$|z| read more here.
Keywords: bohr inequality; class; odd analytic; analytic functions ... See more keywords