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The stability of some linear functional equations
 2004), Art. 49. [ONLINE http://jipam.vu.edu.au/article.php?sid= 381
"... ABSTRACT. In this note, we deal with the Baker’s superstability for the following linear functional equations m∑ f(x + y + ai) = f(x)f(y), x, y ∈ G, i=1 m∑ [f(x + y + ai) + f(x − y − ai)] = 2f(x)f(y), x, y ∈ G, i=1 where G is an abelian group, a1,..., am (m ∈ N) are arbitrary elements in G and f i ..."
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ABSTRACT. In this note, we deal with the Baker’s superstability for the following linear functional equations m∑ f(x + y + ai) = f(x)f(y), x, y ∈ G, i=1 m∑ [f(x + y + ai) + f(x − y − ai)] = 2f(x)f(y), x, y ∈ G, i=1 where G is an abelian group, a1,..., am (m ∈ N) are arbitrary elements in G and f
LINEAR FUNCTIONAL EQUATIONS AND INTERPOLATION SERIES
, 1954
"... 1. Introduction. The question of obtaining complete sets of solutions for a given linear partial differential equation is of the greatest interest from the theoretical as well as from the computational point of view. For constructing such sets, several methods of considerable generality have been pr ..."
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1. Introduction. The question of obtaining complete sets of solutions for a given linear partial differential equation is of the greatest interest from the theoretical as well as from the computational point of view. For constructing such sets, several methods of considerable generality have been
Hyperstability of a class of linear functional equations
 Acta Math. Acad. Paedagogiecae Nyíregyháziensis
"... Abstract. The aim of this note is to offer hyperstability results for linear functional equations of the form f(s) + f(t) = 1 n n∑ i=1 f(sϕi(t)) (s, t ∈ S), where S is a semigroup and where ϕ1,..., ϕn: S → S are pairwise distinct automorphisms of S such that the set {ϕ1,..., ϕn} is a group equipped ..."
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Abstract. The aim of this note is to offer hyperstability results for linear functional equations of the form f(s) + f(t) = 1 n n∑ i=1 f(sϕi(t)) (s, t ∈ S), where S is a semigroup and where ϕ1,..., ϕn: S → S are pairwise distinct automorphisms of S such that the set {ϕ1,..., ϕn} is a group equipped
SOME REMARKS ON STABILITY AND SOLVABILITY OF LINEAR FUNCTIONAL EQUATIONS
"... with the author’s compliments and very good wishes Submitted by T. Riedel Abstract. In the present work we continue studying the solvability of the linear functional equations ∑N j=1cjF ◦ aj = H and also the strong and weak stability of the corresponding operator P (see the definition below). By ana ..."
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with the author’s compliments and very good wishes Submitted by T. Riedel Abstract. In the present work we continue studying the solvability of the linear functional equations ∑N j=1cjF ◦ aj = H and also the strong and weak stability of the corresponding operator P (see the definition below
Algebraic methods for the solution of linear functional equations
"... 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 e ..."
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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
Oscillation Of Linear Functional Equations Of Higher Order
, 1995
"... . The paper contains sufficient conditions under which all solutions of linear functional equations of the higher order are oscillatory. 1. Introduction Let ! be the set of real numbers and let I denote an unbounded subset of !+ = [0; 1). By g m we mean the mth iterate of the function g : I ! I ..."
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. The paper contains sufficient conditions under which all solutions of linear functional equations of the higher order are oscillatory. 1. Introduction Let ! be the set of real numbers and let I denote an unbounded subset of !+ = [0; 1). By g m we mean the mth iterate of the function g : I
and Ashish, On the stability of generalized Cauchy linear functional equations, Int
 J. of Math. Anal
"... Abstract We investigate the following generalized Cauchy linear functional equation where a is an arbitrary number and prove the HyersUlamRassias stability of the functional equations on Banach spaces. Mathematics Subject Classification: 39B52, 39B82, 39B72, 47H09 ..."
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Cited by 2 (2 self)
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Abstract We investigate the following generalized Cauchy linear functional equation where a is an arbitrary number and prove the HyersUlamRassias stability of the functional equations on Banach spaces. Mathematics Subject Classification: 39B52, 39B82, 39B72, 47H09
EXISTENCE OF NONTRIVIAL SOLUTIONS OF LINEAR FUNCTIONAL EQUATIONS
"... Abstract. In this paper we study functional equation n ..."
On analytic solutions of the nonlinear functional equation
"... Abstract, in th e p re se n t p a p e r w e co nsid er th e p ro b lem of th e existence a n d u n iqueness of local an a ly tic solutions of th e eq u atio n rp(fix)) = V(qc>(x))+U(x). T his p a p e r is a co n tin u atio n of 1. In papers [1] and [2] we considered th e problem of the existence ..."
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of the existence and uniqueness of local analytic solutions of equation w here cp is an unknow n function, and analytic functions f, g fulfil the following assumptions: A complex function j is defined and analytic in a neighbourhood of the point zero belonging to the field C of complex num bers and f has 2 ero
Massera Criterion for Linear Functional Equations in a Framework of Hyperfunctions
"... Abstract. We introduce a sheaf of bounded hyperfunctions at infinity in one variable, and consider periodic linear functional equations. We show that a Massera type theorem holds in this framework. Moreover we consider its vectorvalued variants and give applications to partial differential equatio ..."
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Abstract. We introduce a sheaf of bounded hyperfunctions at infinity in one variable, and consider periodic linear functional equations. We show that a Massera type theorem holds in this framework. Moreover we consider its vectorvalued variants and give applications to partial differential
Results 1  10
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123,221