scholarly journals The Bohr Inequality for the Generalized Cesáro Averaging Operators

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Ilgiz R. Kayumov ◽  
Diana M. Khammatova ◽  
Saminathan Ponnusamy
Keyword(s):  
Averaging Operators ◽  
Cesaro Averaging

Adjoint of generalized Cesáro operators on analytic function spaces

2020 ◽  
Vol 26 (2) ◽  
pp. 185-192
Author(s):  
Sunanda Naik ◽  
Pankaj K. Nath
Keyword(s):  
Analytic Function ◽  
Convolution Operator ◽  
Composition Operators ◽  
Mixed Norm ◽  
Averaging Operators ◽  
Mixed Norm Spaces ◽  
Cesaro Averaging ◽  
Analytic Function Spaces ◽  
Appl Math ◽  
Two Parameter

AbstractIn this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular, we obtain a well-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 2009, 2, 304–311]. Also we consider the adjoint {\mathcal{A}^{b,c}} for {b>0} of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces {B_{\alpha+(c-1)}^{p,q}} for {c>1}.

Cesàro averaging operators

1994 ◽  
Vol 124 (1) ◽  
pp. 121-126 ◽  
Author(s):  
Krzysztof Stempak
Keyword(s):  
Sequence Spaces ◽  
Averaging Operators ◽  
Cesaro Averaging

We define a family of Cesàro operators , Reα≧0, and consider the question of their boundedness on Hp spaces. We also consider discrete versions of these operators acting on sequence spaces.

Cesàro averaging operators on Hardy spaces

1996 ◽  
Vol 126 (3) ◽  
pp. 617-624 ◽  
Author(s):  
Kenneth F. Andersen
Keyword(s):  
Hardy Spaces ◽  
Averaging Operators ◽  
Averaging Operator ◽  
Cesaro Averaging ◽  
Open Question

It is shown that the Cesàro averaging operatorℜα > – 1, satisfies an inequality which immediately implies that it is bounded on certain Hardy spaces including Hp, 0 < p < ∞. This answers an open question of Stempak, who introduced these operators and obtained their boundedness on Hp, 0 < p ≦ 2, for ℜα ≧ 0. The operator which is conjugate to on H2 is also shown to be bounded on Hp for 1 < p < ∞ and ℜα = – 1. This extends a result of Stempak who obtained this boundedness for 2 ≦ p≦ ∞ and ℜα ≧:0.

Boundedness of the Cesàro averaging operators on Dirichlet spaces

2004 ◽  
Vol 134 (4) ◽  
pp. 609-616
Author(s):  
Kenneth F. Andersen
Keyword(s):  
Dirichlet Space ◽  
Dirichlet Spaces ◽  
Averaging Operators ◽  
Cesaro Averaging ◽  
Associated Operators

It is shown that the Cesàro averaging operators Cα, Re α > −1, introduced by Stempak, are bounded on the Dirichlet space Da if and only if a > 0, while the associated operators Aα are bounded on Da if and only if −1 < a < 2. This extends results of Galanopoulos, who considered the particular case α = 0 for 0 ≤ a ≤ 1.

scholarly journals Boundedness of generalized Cesáro averaging operators on certain function spaces

2005 ◽  
Vol 180 (2) ◽  
pp. 333-344 ◽  
Author(s):  
M.R. Agrawal ◽  
P.G. Howlett ◽  
S.K. Lucas ◽  
S. Naik ◽  
S. Ponnusamy
Keyword(s):  
Function Spaces ◽  
Averaging Operators ◽  
Cesaro Averaging

scholarly journals Geometric Properties of Cesàro Averaging Operators

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Priyanka Sangal ◽  
A. Swaminathan
Keyword(s):  
Analytic Function ◽  
Unit Disc ◽  
Averaging Operators ◽  
Geometric Properties ◽  
Cesaro Averaging

Using positivity of trigonometric cosine and sine sums whose coefficients are generalization of Vietoris numbers, we find the conditions on coefficient {ak} to characterize the geometric properties of the corresponding analytic function f(z)=z+∑k=2∞akzk in the unit disc D. As an application, we also find geometric properties of generalized Cesàro-type polynomials.

Averaging operators and real equations of hydromechanics

2010 ◽  
Vol 165 (6) ◽  
pp. 637-653 ◽  
Author(s):  
R. R. Aidagulov ◽  
M. V. Shamolin
Keyword(s):  
Averaging Operators

scholarly journals INDUCED AND LOGARITHMIC DISTANCES WITH MULTI-REGION AGGREGATION OPERATORS

2019 ◽  
Vol 0 (0) ◽  
pp. 1-29 ◽  
Author(s):  
Víctor G. Alfaro-García ◽  
José M. Merigó ◽  
Leobardo Plata-Pérez ◽  
Gerardo G. Alfaro-Calderón ◽  
Anna M. Gil-Lafuente
Keyword(s):  
Distance Measure ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Averaging Operators ◽  
Heterogeneous Information ◽  
Weighting Vector ◽  
Choquet Integrals ◽  
World Information ◽  
Logarithmic Distance ◽  
Region Aggregation

This paper introduces the induced ordered weighted logarithmic averaging IOWLAD and multiregion induced ordered weighted logarithmic averaging MR-IOWLAD operators. The distinctive characteristic of these operators lies in the notion of distance measures combined with the complex reordering mechanism of inducing variables and the properties of the logarithmic averaging operators. The main advantage of MR-IOWLAD operators is their design, which is specifically thought to aid in decision-making when a set of diverse regions with different properties must be considered. Moreover, the induced weighting vector and the distance measure mechanisms of the operator allow for the wider modeling of problems, including heterogeneous information and the complex attitudinal character of experts, when aiming for an ideal scenario. Along with analyzing the main properties of the IOWLAD operators, their families and specific cases, we also introduce some extensions, such as the induced generalized ordered weighted averaging IGOWLAD operator and Choquet integrals. We present the induced Choquet logarithmic distance averaging ICLD operator and the generalized induced Choquet logarithmic distance averaging IGCLD operator. Finally, an illustrative example is proposed, including real-world information retrieved from the United Nations World Statistics for global regions.

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