A special class of functional equations
-
Ahmed Charifi
,
Radosław Łukasik
Abstract
We obtain in terms of additive and multi-additive functions the solutions f, h: S → H of the functional equation
where (S, +) is an abelian monoid, Φ is a finite group of automorphisms of S, N = | Φ | designates the number of its elements, {aλ, λ ∈ Φ} are arbitrary elements of S and (H, +) is an abelian group. In addition, some applications are given. This equation provides a joint generalization of many functional equations such as Cauchy’s, Jensen’s, Łukasik’s, quadratic or Φ-quadratic equations.
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© 2018 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- On the family of functions with closure of graphs in the Mendez ideals
- The predicate completion of a partial information system
- On lattices of z-ideals of function rings
- Compactifications of partial frames via strongly regular ideals
- Lifting components in clean abelian ℓ-groups
- Invariance of nonatomic measures on effect algebras
- On the alexander dual of path ideals of cycle posets
- Generalized multiplicative derivations in 3-prime near rings
- Cleft extensions for quasi-entwining structures
- Groups with positive rank gradient and their actions
- Certain results on q-starlike and q-convex error functions
- Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
- Positive periodic solutions for singular high-order neutral functional differential equations
- A special class of functional equations
- Matrix mappings and general bounded linear operators on the space bv
- Skew-symmetric operators and reflexivity
- Derivatives of Hadamard type in vector optimization
- Cardinal functions of the hyperspace of convergent sequences
- Suzuki-type of common fixed point theorems in fuzzy metric spaces
- Second hankel determinat for certain analytic functions satisfying subordinate condition
