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http://dx.doi.org/10.7468/jksmeb.2021.28.4.387

ON THE SUPERSTABILITY OF THE p-RADICAL SINE TYPE FUNCTIONAL EQUATIONS  

Kim, Gwang Hui (Department of Applied Mathematics, Kangnam University)
Publication Information
The Pure and Applied Mathematics / v.28, no.4, 2021 , pp. 387-398 More about this Journal
Abstract
In this paper, we will find solutions and investigate the superstability bounded by constant for the p-radical functional equations as follows: $f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=\;\{(i)\;f(x)f(y),\\(ii)\;g(x)f(y),\\(iii)\;f(x)g(y),\\(iv)\;g(x)g(y).$ with respect to the sine functional equation, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebra.
Keywords
stability; superstability; sine functional equation; cosine functional equation; p-radical functional equation;
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Times Cited By KSCI : 1  (Citation Analysis)
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