We introduce the definition of non-Archimedean 2-fuzzy 2-normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. And then we can get isome...We introduce the definition of non-Archimedean 2-fuzzy 2-normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. And then we can get isometry when a mapping satisfies AOPP and (*) (in article) by applying the Benz’s theorem about the Aleksandrov problem in non-Archimedean 2-fuzzy 2-normed spaces.展开更多
We shall introduce 1-type Lipschitz multifunctions from R into generalized 2-normed spaces, and give some results about their 1-type Lipschitz selections.
The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-norm...The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.展开更多
In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …...In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …, 5}, a_1,…, a_k are fixed nonzero reals when p ∈ {1,3,5} and are fixed positive reals when p ∈{2,4}.展开更多
The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space....The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.展开更多
The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable ...The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.展开更多
In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a m...In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a mapping from a commutative group(G,+)to a 2-Banach space(Y,||·,·||).Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk,K Ciepliński.On a fixed point theorem in 2-normed spaces and some of its applications.Acta Mathematica Scientia,2018,38B(2):377-390].展开更多
In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the co...In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the continuity of vector space operations is discussed and it is proved that the vector space with I-topology τ‖.,.‖ is not I-topological vector space but with τ*‖.,.‖ is I-topological vector space.Next we study the relationship between this two I-topologies and it is proved that τ*‖.,.‖■τ‖.,.‖.展开更多
文摘We introduce the definition of non-Archimedean 2-fuzzy 2-normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. And then we can get isometry when a mapping satisfies AOPP and (*) (in article) by applying the Benz’s theorem about the Aleksandrov problem in non-Archimedean 2-fuzzy 2-normed spaces.
文摘We shall introduce 1-type Lipschitz multifunctions from R into generalized 2-normed spaces, and give some results about their 1-type Lipschitz selections.
文摘The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.
文摘In this paper, using the Brzdek's fixed point theorem [9,Theorem 1] in non-Archimedean(2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation ■where p∈{1, …, 5}, a_1,…, a_k are fixed nonzero reals when p ∈ {1,3,5} and are fixed positive reals when p ∈{2,4}.
文摘The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.
文摘The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.
基金This work was supported by Research Professional Development Project under the Science Achievement Scholarship of Thailand(SAST)and Thammasat University Research Fund,Contract No.TUGG 33/2562The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under grant no.MRG6180283 for financial support during the preparation of this manuscript.
文摘In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a mapping from a commutative group(G,+)to a 2-Banach space(Y,||·,·||).Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk,K Ciepliński.On a fixed point theorem in 2-normed spaces and some of its applications.Acta Mathematica Scientia,2018,38B(2):377-390].
文摘In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the continuity of vector space operations is discussed and it is proved that the vector space with I-topology τ‖.,.‖ is not I-topological vector space but with τ*‖.,.‖ is I-topological vector space.Next we study the relationship between this two I-topologies and it is proved that τ*‖.,.‖■τ‖.,.‖.
