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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Academic Publications, Ltd.
2017
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| Subjects: | |
| Online Access: | https://repo.uum.edu.my/id/eprint/21982/1/IJPAM%20112%203%202017%20461%20488.pdf |
| _version_ | 1825804661811052544 |
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| 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 |
| collection | UUM |
| 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]. |
| first_indexed | 2024-07-04T06:19:19Z |
| format | Article |
| id | uum-21982 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T06:19:19Z |
| publishDate | 2017 |
| publisher | Academic Publications, Ltd. |
| record_format | eprints |
| spelling | uum-219822017-05-07T07:16:35Z https://repo.uum.edu.my/id/eprint/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 https://repo.uum.edu.my/id/eprint/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 doi:10.12732/ijpam.v112i3.3 |
| spellingShingle | QA Mathematics Akhadkulov, Habibulla Mohd Salmi, Noorani Saaban, Azizan Akhatkulov, Sokhobiddin Notes on zygmund functions |
| title | Notes on zygmund functions |
| title_full | Notes on zygmund functions |
| title_fullStr | Notes on zygmund functions |
| title_full_unstemmed | Notes on zygmund functions |
| title_short | Notes on zygmund functions |
| title_sort | notes on zygmund functions |
| topic | QA Mathematics |
| url | https://repo.uum.edu.my/id/eprint/21982/1/IJPAM%20112%203%202017%20461%20488.pdf |
| work_keys_str_mv | AT akhadkulovhabibulla notesonzygmundfunctions AT mohdsalminoorani notesonzygmundfunctions AT saabanazizan notesonzygmundfunctions AT akhatkulovsokhobiddin notesonzygmundfunctions |