On a Functional Equation Containing Weighted Arithmetic Means

Varga, Adrienn

doi:10.1007/978-3-7643-8773-0_30

Cited by 8 publications

(7 citation statements)

References 6 publications

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“…It is known [10] that there exists a field isomorphism The proof goes back to the construction of a field homomorphism δ 1 satisfying (F 1 ). Using δ −1 1 the role of the outer and the inner parameters in Theorem 2.1 can be interchanged; for the details see [9].…”

Section: Preliminary Results and Basic Conceptsmentioning

confidence: 99%

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Nontrivial solutions of linear functional equations: methods and examples

Varga¹,

Vincze²

2015

OpMath

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Abstract. For a wide class of linear functional equations the solutions are generalized polynomials. The existence of non-trivial monomial terms of the solution strongly depends on the algebraic properties of some related families of parameters. As a continuation of the previous work [A. Varga, Cs. Vincze, G. Kiss, Algebraic methods for the solution of linear functional equations, Acta Math. Hungar.] we are going to present constructive algebraic methods of the solution in some special cases. Explicit examples will be also given.

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Section: Preliminary Results and Basic Conceptsmentioning

confidence: 99%

“…. , n − 1); for details see [10] and [11]. The problem is to find necessary and sufficient conditions in terms of the parameters α 1 , .…”

Section: Introduction Consider Functional Equationmentioning

confidence: 99%

Nontrivial solutions of linear functional equations: methods and examples

Varga¹,

Vincze²

2015

OpMath

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“…For the proof see Lemma 3.1. in [4]. Now we can use the procedure of semilinear extension to construct a not identically zero additive function A such that A(…”

Section: About the Remaining Casementioning

confidence: 99%

“…The theory of functional equations containing weighted arithmetic means gives motivations to investigate (1.1) (see [4]). …”

Section: Introductionmentioning

confidence: 99%

On additive solutions of a linear equation

Varga

2009

Acta Math Hung

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“…A. Varga and Cs. Vincze [4] applied some field homomorphisms to construct non-trivial solutions. The method leads naturally to the problem of algebraic characterization [3].…”

Section: Introductionmentioning

confidence: 99%

Algebraic methods for the solution of linear functional equations

2015

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belongs to the class of linear functional equations. The solutions form a linear space with respect to the usual pointwise operations. According to the classical results of the theory they must be generalized polynomials. New investigations have been started few years ago. They clarified that the existence of non-trivial solutions depends on the algebraic properties of some related families of parameters. The problem is to find the necessary and sufficient conditions for the existence of non-trivial solutions in terms of these kinds of properties. One of the most earlier results is due to Z. Daróczy [1]. It can be considered as the solution of the problem in case of n = 2. We are going to take more steps forward by solving the problem in case of n = 3.

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On a Functional Equation Containing Weighted Arithmetic Means

Cited by 8 publications

References 6 publications

Nontrivial solutions of linear functional equations: methods and examples

Nontrivial solutions of linear functional equations: methods and examples

On additive solutions of a linear equation

Algebraic methods for the solution of linear functional equations

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