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whose solution is said to be a generalized additive mapping of Euler-Lagrange type.
Recently, Park and Park [59] introduced and investigated the following additive functional equation of Euler-Lagrange type: (1.2). whose solution is said to be a generalized additive mapping of Euler-Lagrange type.
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So, A is a generalized additive set-valued mapping.
Then we claim that A is a generalized additive set-valued mapping.
Since L is a generalized additive mapping, from Lemma 4.1 it follows that L is additive, and therefore, L ( u x ) = r L ( u x r ) = u L ( x ), u ∈ U ( A ), x ∈ X.
(any solution of (1.1) will be called a generalized additive mapping) and proved its Hyers-Ulam stability in Banach modules over a unital C ∗ -algebra via the direct method.
Every solution of the generalized additive set-valued functional equation is called a generalized additive set-valued mapping.
where Every solution of the functional equation (1.9) is said to be a generalized Euler-Lagrange type additive mapping.
where r 1, …, r n ∈ R. Every solution of the functional equation (1.3) is said to be a generalized Euler-Lagrange type additive mapping.
The penalized splines can be estimated in a generalized additive model using R software (R Foundation for Statistical Computing 2006).
This allowed the detection function to be estimated in a generalized additive modelling framework.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com