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Lattictic non-archimedean random stability of ACQ functional equationKeywords: Stability , Random normed space , Fixed point , Generalized Hyers-Ulam stability , Additive-cubic-quartic functional equation , Lattice , non-Archimedean normed spaces Abstract: In this paper, we prove the generalized Hyers-Ulam stability of the following additive-cubic-quartic functional equation 1 1 f ( x + 2 y ) + 1 1 f ( x - 2 y ) = 4 4 f ( x + y ) + 4 4 f ( x - y ) + 1 2 f ( 3 y ) - 4 8 f ( 2 y ) + 6 0 f ( y ) - 6 6 f ( x ) in various complete lattictic random normed spaces. Mathematics Subject Classification (2000) Primary 54E40; Secondary 39B82, 46S50, 46S40.
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