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The stability problem of functional equations can be determined on various domains of functions.
For r = 1, the stability problem of Equation (1.4) has been investigated by Cholewa [15].
In 1993, Obloza [1] first initiated the study of the Ulam stability problem of differential equations.
For r = 2, the stability problem of Equation (1.4) has been proved by Rassias [16].
This is the first result for the stability problem of functional equations in 2-Banach spaces.
We now investigate the generalized Hyers-Ulam stability problem of the functional equation (1.3).
This section addresses the exponential stability problem of the switched system (2.7).
The stability problem of functional equations has been extensively investigated by some mathematicians (see [30 46]).
When (k=0), the stability problem of solitary waves was solved in [10].
The stability problem of functional equations had been first raised by Ulam [1].
This topic of research plays an important role in the stability problem of fixed point iterations.
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