Open AccessOn the stability of multicubic-quartic and multimixed cubic-quartic mappings
Author(s) -
Zohreh Abbasbeygi,
Abasalt Bodaghi,
Ayoub Gharibkhajeh
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2203031a
Subject(s) - quartic function , quartic surface , mathematics , cubic function , quartic plane curve , corollary , stability (learning theory) , quintic function , pure mathematics , mathematical analysis , nonlinear system , physics , computer science , quantum mechanics , machine learning
In this paper, we define the multicubic-quartic and the multimixed cubic-quartic mappings and characterize them. In other words, we unify the system of functional equations defining a multimixed cubic-quartic (resp., multicubic-quartic) mapping to a single equation, namely, the multimixed cubic-quartic (resp., multicubic-quartic) functional equation. We also show that under what conditions a multimixed cubic-quartic mapping can be multicubic, multiquartic and multicubic-quartic. Moreover, by using a fixed point theorem, we study the generalized Hyers-Ulam stability of multimixed cubic-quartic functional equations in non-Archimedean normed spaces. As a corollary, we show that every multimixed cubicquartic mapping under some mild conditions can be hyperstable. Lastly, we present a non-stable example for the multiquartic mappings.