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ScienceAsia 42(2016): 296-301 |doi: 10.2306/scienceasia1513-1874.2016.42.296

Stability of Fréchet's functional equation on certain groupoids

Teerapol Sukhonwimolmal, Paisan Nakmahachalasint*, Patanee Udomkavanich

ABSTRACT:     We obtain a Hyers-Ulam stability result for Fréchet's functional equation Δn+1y1,y2,...,yn+1f(x)=0 for all x,y1,y2,...,yn+1G, where f:GB is a mapping from a power-associative, mth-power-symmetric groupoid with a left identity into a real Banach space, and m,n are nonnegative integers with m>1.

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Department of Mathematics and Computer Science, Chulalongkorn University, Bangkok 10330 Thailand

* Corresponding author, E-mail: Paisan.N@chula.ac.th

Received 17 Mar 2016, Accepted 1 Aug 2016