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Notes on zygmund functions

In this paper we study a class of continuous functions satisfying a certain Zyg-mund condition dependent on a parameter γ > 0. It shown that the modulus of continuity of such functions is O(δ(log 1/δ)1-γ) if ∈ (0, 1) and O(δ(log log 1/δ )) if γ = 1. Moreover, these functions are differentiable if...

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Main Authors: Akhadkulov, Habibulla, Mohd Salmi, Noorani, Saaban, Azizan, Akhatkulov, Sokhobiddin
Format: Article
Language:English
Published: Academic Publications, Ltd. 2017
Subjects:
QA Mathematics
Online Access:http://repo.uum.edu.my/21982/1/IJPAM%20112%203%202017%20461%20488.pdf
http://repo.uum.edu.my/21982/
http://doi.org/10.12732/ijpam.v112i3.3
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spelling my.uum.repo.219822017-05-07T07:16:35Z http://repo.uum.edu.my/21982/ Notes on zygmund functions Akhadkulov, Habibulla Mohd Salmi, Noorani Saaban, Azizan Akhatkulov, Sokhobiddin QA Mathematics In this paper we study a class of continuous functions satisfying a certain Zyg-mund condition dependent on a parameter γ > 0. It shown that the modulus of continuity of such functions is O(δ(log 1/δ)1-γ) if ∈ (0, 1) and O(δ(log log 1/δ )) if γ = 1. Moreover, these functions are differentiable if γ > 1. These results extend the results in literatures [4], [5]. Academic Publications, Ltd. 2017 Article PeerReviewed application/pdf en cc4_by http://repo.uum.edu.my/21982/1/IJPAM%20112%203%202017%20461%20488.pdf Akhadkulov, Habibulla and Mohd Salmi, Noorani and Saaban, Azizan and Akhatkulov, Sokhobiddin (2017) Notes on zygmund functions. International Journal of Pure and Applied Mathematics, 112 (3). pp. 481-488. ISSN 1311-8080 http://doi.org/10.12732/ijpam.v112i3.3 doi:10.12732/ijpam.v112i3.3
institution Universiti Utara Malaysia
building UUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Utara Malaysia
content_source UUM Institutionali Repository
url_provider http://repo.uum.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Akhadkulov, Habibulla
Mohd Salmi, Noorani
Saaban, Azizan
Akhatkulov, Sokhobiddin
Notes on zygmund functions
description In this paper we study a class of continuous functions satisfying a certain Zyg-mund condition dependent on a parameter γ > 0. It shown that the modulus of continuity of such functions is O(δ(log 1/δ)1-γ) if ∈ (0, 1) and O(δ(log log 1/δ )) if γ = 1. Moreover, these functions are differentiable if γ > 1. These results extend the results in literatures [4], [5].
format Article
author Akhadkulov, Habibulla
Mohd Salmi, Noorani
Saaban, Azizan
Akhatkulov, Sokhobiddin
author_facet Akhadkulov, Habibulla
Mohd Salmi, Noorani
Saaban, Azizan
Akhatkulov, Sokhobiddin
author_sort Akhadkulov, Habibulla
title Notes on zygmund functions
title_short Notes on zygmund functions
title_full Notes on zygmund functions
title_fullStr Notes on zygmund functions
title_full_unstemmed Notes on zygmund functions
title_sort notes on zygmund functions
publisher Academic Publications, Ltd.
publishDate 2017
url http://repo.uum.edu.my/21982/1/IJPAM%20112%203%202017%20461%20488.pdf
http://repo.uum.edu.my/21982/
http://doi.org/10.12732/ijpam.v112i3.3
_version_ 1644283391756992512
score 13.211869

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