Abstract
Abstract Using the fixed point method, we investigate the stability of the system of additive, quadratic and quartic functional equations with constant coefficients in non-Archimedean normed spaces. Also, we give an example to show that some results in the stability of functional equations in (Archimedean) normed spaces are not valid in non-Archimedean normed spaces. MSC:39B82, 46S10, 47H10.
Highlights
1 Introduction The stability problems concerning group homomorphisms was raised by Ulam [ ] in and affirmatively answered for Banach spaces by Hyers [ ] in the year
In, a generalization of the Rassias theorem was obtained by Găvruta [ ] by replacing the unbounded Cauchy difference by a general control function
We investigate the Hyers-Ulam stability for the system of additive, quadratic and quartic functional equations
Summary
The stability problems concerning group homomorphisms was raised by Ulam [ ] in and affirmatively answered for Banach spaces by Hyers [ ] in the year. One may note that |n| ≤ in each valuation field, every triangle is isosceles and there may be no unit vector in a non-Archimedean normed space; cf [ ]. If the condition (iii) in the definition of a valuation mapping is replaced with (iii) |a + b| ≤ max |a|, |b| , the valuation | · | is said to be non-Archimedean.
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