# ON THE STABILITY OF RECIPROCAL-NEGATIVE FERMAT'S EQUATION IN QUASI-β-NORMED SPACES

Kang, Dongseung;Kim, Hoewoon B.

• Accepted : 2019.04.03
• Published : 2019.05.31
• 18 1

#### Abstract

In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

#### Keywords

generalized Hyers-Ulam stability;reciprocal-negative Fermat's equation;${\beta}-normed$ space