scholarly journals Growth of analytic functions in an ultrametric open disk and branched values

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Kamal Boussaf ◽  
Alain Escassut
Keyword(s):  
Analytic Functions ◽  
Open Disk

Simultaneous Automorphisms in Spaces of Analytic Functions

1963 ◽  
Vol 15 ◽  
pp. 495-502
Author(s):  
A. Alexiewicz ◽  
M. G. Arsove
Keyword(s):  
Uniform Convergence ◽  
Analytic Functions ◽  
Fréchet Space ◽  
Frechet Space ◽  
Open Disk ◽  
Compact Sets ◽  
Spaces Of Analytic Functions

Two spaces of analytic functions are considered, each comprised of functions analytic on the open disk NR(0) of radius R (0 < R < +∞ ) centred at the origin. The first space consists of all analytic functions on NR(0) topologized according to the metric of uniform convergence on compact sets. As the second space we allow any Fréchet space of analytic functions on NR(0) for which the topology is stronger than that induced by . Our objective is then to present a scheme for constructing simultaneous automorphisms on and .

scholarly journals Certain subclasses of analytic functions associated with fractional $q$-calculus operators

2011 ◽  
Vol 109 (1) ◽  
pp. 55 ◽  
Author(s):  
Sunil Dutt Purohit ◽  
Ravinder Krishna Raina
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Open Disk ◽  
Q Theory ◽  
Special Cases ◽  
Coefficient Inequalities ◽  
Distortion Theorems

We first define the $q$-analogue operators of fractional calculus which are then used in defining certain classes of functions analytic in the open disk. The results investigated for these classes of functions include the coefficient inequalities and some distortion theorems. The results provide extensions of various known results in the $q$-theory of analytic functions. Special cases of our results are pointed out briefly.

scholarly journals URSCM OR BI-URSCM FOR p-ADIC ANALYTIC OR MEROMORPHIC FUNCTIONS INSIDE A DISK

2007 ◽  
Vol 49 (1) ◽  
pp. 121-126
Author(s):  
ABDELBAKI BOUTABAA ◽  
ALAIN ESCASSUT
Keyword(s):  
General Result ◽  
Analytic Functions ◽  
Characteristic Zero ◽  
Meromorphic Functions ◽  
Closed Field ◽  
Open Disk ◽  
Second Main Theorem ◽  
Absolute Value ◽  
Small Functions

Abstract.Let K be an algebraically closed field of characteristic zero, complete with respect to an ultrametric absolute value. In a previous paper, we had found URSCM of 7 points for the whole set of unbounded analytic functions inside an open disk. Here we show the existence of URSCM of 5 points for the same set of functions. We notice a characterization of BI-URSCM of 4 points (and infinity) for meromorphic functions in K and can find BI-URSCM for unbounded meromorphic functions with 9 points (and infinity). The method is based on the p-Adic Nevanlinna Second Main Theorem on 3 Small Functions applied to unbounded analytic and meromorphic functions inside an open disk and we show a more general result based upon the hypothesis of a finite symmetric difference on sets of zeros, counting multiplicities.

scholarly journals Bounds of coefficients for classes of analytic functions related to hypergeometric functions

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3035-3045
Author(s):  
Zhenhan Tu ◽  
Liangpeng Xiong
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Differential Subordination ◽  
Uniformly Convex ◽  
Generalized Hypergeometric Function ◽  
Open Disk ◽  
Starlike And Convex Functions ◽  
Conic Domain

The main purpose of the present paper is to give some sharp coefficients bounds for a certain class of univalent analytic functions in unit open disk, which was defined by using principle of differential subordination and generalized hypergeometric function. As applications, we investigate the almost starlike-type functions, parabolic starlike-type functions and uniformly convex-type functions with conic domain. Our results extend some earlier works related to Ma-Minda starlike and convex functions.

scholarly journals Certain Classes of Analytic Functions Bound with Kober Operators in q -Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
S. D. Purohit ◽  
M. M. Gour ◽  
S. Joshi ◽  
D. L. Suthar
Keyword(s):  
Analytic Functions ◽  
Open Disk ◽  
Coefficient Inequality ◽  
Analytical Functions ◽  
Distortion Theorems

Through applying the Kober fractional q -calculus apprehension, we preliminary implant and introduce new types of univalent analytical functions with a q -differintegral operator in the open disk U = ξ ∈ ℂ : ∣ ξ | < 1 . The coefficient inequality and distortion theorems are among the results examined with these forms of functions. Specific cases are responded and addressed immediately. The findings include an expansion of the numerous established results in the q -theory of analytical functions.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions
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