Abstract
The purpose of this paper is to obtain refined stability results and alternative stability results for additive and quadratic functional equations using direct method in modular spaces.
Highlights
The theory of modulars on linear spaces and the related theory of modular linear spaces have been established by Nakano in [ ]
By using the direct method, we present stability results and alternative stability results of additive functional equations and of quadratic functional equations which are refined versions of Sadeghi [ ], and Wongkum, Chaipunya and Kumam [ ]
2 Stability of additive functional equations in modular spaces Throughout this paper, we assume that V is a linear space and Xρ is a ρ-complete convex modular space
Summary
The theory of modulars on linear spaces and the related theory of modular linear spaces have been established by Nakano in [ ]. It is said that the modular ρ has the Fatou property if and only if ρ(x) ≤ lim infn→∞ ρ(xn) whenever the sequence {xn} is ρ-convergent to x in modular space Xρ . Many authors have investigated the stability using fixed point theorem of quasicontraction mappings in modular spaces without -condition, which has been introduced by Khamsi [ ].
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