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2012•The Pure and Applied MathematicsOpen access

APPROXIMATE PEXIDERIZED EXPONENTIAL TYPE FUNCTIONS

Young-Whan Lee

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Abstract

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$ . From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$ .

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What this paper is about

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$ . From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$ .

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Available abstract

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$ . From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$ .

Key concepts: Exponential function, Exponential type, Type (biology), Mathematics, Function (biology), Double exponential function, Exponential formula, Functional equation

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