Abstract
The aim of this paper is to study the generalized Hyers-Ulam stability of a form of reciprocal-cubic and reciprocal-quartic functional equations in non-Archimedean fields. Some related examples for the singular cases of these new functional equations on an Archimedean field are indicated.
Highlights
1 Introduction The study of the stability of functional equations was instigated by the famous question of Ulam [ ] during a Mathematical Colloquium at the University of Wiskonsin in the year
After that several stability articles, many textbooks and research monographs have investigated the result for various functional equations, for mappings with more general domains and ranges; for instance, see [ – ] and [ ]
The other results pertaining to the stability of different reciprocal-type functional equations can be found in [ – ] and [ ]
Summary
The study of the stability of functional equations was instigated by the famous question of Ulam [ ] during a Mathematical Colloquium at the University of Wiskonsin in the year. In , Ravi and Senthil Kumar [ ] obtained Ulam-Găvruta-Rassias stability for the Rassias reciprocal functional equation r(x)r(y) r(x + y) = Kim et al Advances in Difference Equations (2017) 2017:77 where k > is a positive integer, and investigated its generalized Hyers-Ulam stability in non-Archimedean fields.
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