The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group...The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.展开更多
In this paper, we establish fuzzy stability of the orthogonal Cauchy functional equations f(x + y) = f(x) + f(y), x ⊥ y and the orthogonal Cauchy functional of P exider type f(x + y) = g(x) + h(y), x ⊥ y in which ⊥...In this paper, we establish fuzzy stability of the orthogonal Cauchy functional equations f(x + y) = f(x) + f(y), x ⊥ y and the orthogonal Cauchy functional of P exider type f(x + y) = g(x) + h(y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rtz.展开更多
We consider a class of n-dimensional Pompeiu equations and that of Pexider equations and their Hyers Ulam stability problems in the spaces of Schwartz distributions. First, reducing the given distribution version of f...We consider a class of n-dimensional Pompeiu equations and that of Pexider equations and their Hyers Ulam stability problems in the spaces of Schwartz distributions. First, reducing the given distribution version of functional equations to differential equations we find their solutions. Secondly, using approximate identities we prove the Hyers Ulam stability of the equations.展开更多
In this paper, we investigate the stability of functional equation given by the pseudoadditive mappings of the mixed quadratic and Pexider type in the spirit of Hyers, Ulam, Rassias and Gavruta.
文摘The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.
基金Supported by Opening Foundation of Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing(Grant No.2017CSOBDP0103)Guangxi Universitys Science and Technology Research Project(Grant No.201012MS185)Science and Technology Foundation of Guizhou Province(Grant No.LKS[2012]34)
文摘In this paper, we establish fuzzy stability of the orthogonal Cauchy functional equations f(x + y) = f(x) + f(y), x ⊥ y and the orthogonal Cauchy functional of P exider type f(x + y) = g(x) + h(y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rtz.
基金the Korean Research Foundation Grant funded by the Korean Government(MOEHRD,Basic Research Promotion Fund)(KRF-2005-015-C00026)
文摘We consider a class of n-dimensional Pompeiu equations and that of Pexider equations and their Hyers Ulam stability problems in the spaces of Schwartz distributions. First, reducing the given distribution version of functional equations to differential equations we find their solutions. Secondly, using approximate identities we prove the Hyers Ulam stability of the equations.
文摘In this paper, we investigate the stability of functional equation given by the pseudoadditive mappings of the mixed quadratic and Pexider type in the spirit of Hyers, Ulam, Rassias and Gavruta.
