Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain
Let be the set of real numbers, , , and . As classical and versions of the Hyers-Ulam stability of the logarithmic type functional equation in a restricted domain, we consider the following inequalities: , and in the sectors . As consequences of the results, we obtain asymptotic behaviors of the...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/751680 |
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| _version_ | 1832545300635451392 |
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| author | Jaeyoung Chung Prasanna K. Sahoo |
| author_facet | Jaeyoung Chung Prasanna K. Sahoo |
| author_sort | Jaeyoung Chung |
| collection | DOAJ |
| description | Let be the set of real numbers, , , and . As classical and versions of the Hyers-Ulam stability of the logarithmic type functional equation in a restricted domain, we consider the following inequalities: , and in the sectors . As consequences of the results, we obtain asymptotic behaviors of the previous inequalities. We also consider its distributional version , where , , , , , and the inequality means that for all test functions . |
| format | Article |
| id | doaj-art-4632f1c6262c4ba5873427f3ddcb1809 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4632f1c6262c4ba5873427f3ddcb18092025-02-03T07:26:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/751680751680Stability of a Logarithmic Functional Equation in Distributions on a Restricted DomainJaeyoung Chung0Prasanna K. Sahoo1Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of KoreaDepartment of Mathematics, University of Louisville, Louisville, KY 40292, USALet be the set of real numbers, , , and . As classical and versions of the Hyers-Ulam stability of the logarithmic type functional equation in a restricted domain, we consider the following inequalities: , and in the sectors . As consequences of the results, we obtain asymptotic behaviors of the previous inequalities. We also consider its distributional version , where , , , , , and the inequality means that for all test functions .http://dx.doi.org/10.1155/2013/751680 |
| spellingShingle | Jaeyoung Chung Prasanna K. Sahoo Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain Abstract and Applied Analysis |
| title | Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain |
| title_full | Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain |
| title_fullStr | Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain |
| title_full_unstemmed | Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain |
| title_short | Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain |
| title_sort | stability of a logarithmic functional equation in distributions on a restricted domain |
| url | http://dx.doi.org/10.1155/2013/751680 |
| work_keys_str_mv | AT jaeyoungchung stabilityofalogarithmicfunctionalequationindistributionsonarestricteddomain AT prasannaksahoo stabilityofalogarithmicfunctionalequationindistributionsonarestricteddomain |