In this article, we prove, both in complete non-Archimedean normed spaces and in 2-Banach spaces, the generalized Hyers-Ulam stability of an equation characterizing multi- quadratic mappings. Our results generalize so...In this article, we prove, both in complete non-Archimedean normed spaces and in 2-Banach spaces, the generalized Hyers-Ulam stability of an equation characterizing multi- quadratic mappings. Our results generalize some known outcomes.展开更多
In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point...In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.展开更多
In this paper we unify the system of functional equations defining multi-quadratic mappings to a single equation, find out the general solution of it and prove its generalized Hyers-Ulam stability.
In this article, the author presents some results of the isometric linear extension from some spheres in the finite dimensional space s（n）. Moreover, the author presents the representation for the onto isometric map...In this article, the author presents some results of the isometric linear extension from some spheres in the finite dimensional space s（n）. Moreover, the author presents the representation for the onto isometric mappings in the space s. It is obtained that if V is a surjective isometry from the space s onto s with V（0） = 0, then V must be real linear.展开更多
Using the fixed point method, this article proves the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by t...Using the fixed point method, this article proves the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by the quadratic functional equation of Apollonius type.展开更多
文摘In this article, we prove, both in complete non-Archimedean normed spaces and in 2-Banach spaces, the generalized Hyers-Ulam stability of an equation characterizing multi- quadratic mappings. Our results generalize some known outcomes.
文摘In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.
基金Supported by the National Natural Science Foundation of China(Grant No.10971117)
文摘In this paper we unify the system of functional equations defining multi-quadratic mappings to a single equation, find out the general solution of it and prove its generalized Hyers-Ulam stability.
基金Supported by the National Natural Science Foundation of China (11001134 , 11126250)the Fundamental Research Funds for the Central Universitiesthe Tianjin Science & Technology Fund (20100820)
基金Supported by the National Science Foundation of China (10571090) The Research Fund for the Doctoral Program of Higher Education (20010055013)
文摘In this article, the author presents some results of the isometric linear extension from some spheres in the finite dimensional space s（n）. Moreover, the author presents the representation for the onto isometric mappings in the space s. It is obtained that if V is a surjective isometry from the space s onto s with V（0） = 0, then V must be real linear.
文摘Using the fixed point method, this article proves the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by the quadratic functional equation of Apollonius type.
