Abstract
In this paper we prove the generalized Hyers-Ulam stability of the system defining general Euler-Lagrange quadratic mappings in non-Archimedean fuzzy normed spaces over a field with valuation using the direct and the fixed point methods.MSC:39B82, 39B52, 46H25.
Highlights
A field endowed with a valuation mapping will be called a valued field
The main purpose of this paper is to prove the generalized Hyers-Ulam stability of multiEuler-Lagrange quadratic functional equation ( . ) in complete non-Archimedean fuzzy normed spaces over a field with valuation using the direct and the fixed point methods
3 Stability of the functional equation (1.1): a direct method Throughout this section, using a direct method, we prove the stability of Eq ( . ) in complete non-Archimedean fuzzy normed spaces
Summary
) in complete non-Archimedean fuzzy normed spaces over a field with valuation using the direct and the fixed point methods. Let X be a linear space over a field K with a non-Archimedean valuation | · |. A function · : X → [ , ∞) is said to be a non-Archimedean norm if it satisfies the following conditions:. Let (X , N, T) be a non-Archimedean fuzzy normed space. . If every Cauchy sequence in X is convergent, the space is called a complete non-Archimedean fuzzy normed space. If (X , · ) is complete, (X , N, TP) is complete and it is a complete non-Archimedean fuzzy normed space over an Archimedean valued field. Let K be a valued field, X be a vector space over K and (Y, N, T) be a complete non-Archimedean fuzzy normed space over K. ≥ T i(x , . . . , xi, , xi+ , . . . , xn, |λ|t), i x , . . . , xi– , axi, bxi, xi+ , . . . , xn, |λ| t
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
