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Volume 6, Issue 2, Article 32 |
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On Hyers-Ulam Stability of a Special Case of O'Connor's and Gajda's Functional Equations
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Authors: |
Belaid Bouikhalene, Elhoucien Elqorachi, Ahmed Redouani, |
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Keywords:
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Functional equations, Hyers-Ulam stability, Gelfand pairs. |
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Date Received:
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08/11/04 |
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Date Accepted:
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01/03/05 |
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Subject Codes: |
39B72.
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Editors: |
Kazimierz Nikodem, |
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Abstract: |
In this paper, we obtain the Hyers-Ulam stability for the following functional equation where is a locally compact group, is a compact subgroup of , is the normalized Haar measure of , is a finite group of -invariant morphisms of and are continuous complex-valued functions such that satisfies the Kannappan type condition ![$displaystyle int_{K}int_{K}f(zkxk^{-1}hyh^{-1})domega _{K}(k)domega _{K}(h)=int_{K}int_{K}f(zkyk^{-1}hxh^{-1})domega_{K}(k)domega _{K}(h),$](images/213_04_JIPAM/img8.gif) | (*) | for all
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