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Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain

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  • Jaeyoung Chung
  • Prasanna K. Sahoo

Abstract

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 .

Suggested Citation

  • Jaeyoung Chung & Prasanna K. Sahoo, 2013. "Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, September.
    • Handle: RePEc:hin:jnlaaa:751680
    DOI: 10.1155/2013/751680
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