Let n≥2 be an integer number. In this paper, we investigate the generalized Hyers Ulam- Rassias stability in Banach spaces and also Banach modules over a Banach algebra and a C＊-algebra and the stability using the a...Let n≥2 be an integer number. In this paper, we investigate the generalized Hyers Ulam- Rassias stability in Banach spaces and also Banach modules over a Banach algebra and a C＊-algebra and the stability using the alternative fixed point of an n-dimensional cubic functional equation in Banach spaces：f（2∑j=1^n-1 xj＋xn）＋f（2∑j=1^n-1 xj-xn）＋4∑j=1^n-1f（xj）=16f（∑j=1^n-1 xj）＋2∑j=1^n-1（f（xj＋xn）＋f（xj-xn）展开更多
In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation2f（x ＋ 2y） ＋ f（2x - y） = 5f（x ＋ y） ＋ 5f（x...In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation2f（x ＋ 2y） ＋ f（2x - y） = 5f（x ＋ y） ＋ 5f（x - y）＋ 15f（y）in the spirit of Hyers, Ulam, Rassias and Gavruta.展开更多
In this paper, we establish the general solution and the generalized Hyers-Ulam-Rassias stability problem for a cubic Jensen-type functional equation,4f（（3x＋y）/4）＋4f（（x＋3y）/4）=6f（（x＋y）/2）＋f（x）＋f（y...In this paper, we establish the general solution and the generalized Hyers-Ulam-Rassias stability problem for a cubic Jensen-type functional equation,4f（（3x＋y）/4）＋4f（（x＋3y）/4）=6f（（x＋y）/2）＋f（x）＋f（y）,9f（（2x＋y/3）＋9f（（x＋2y）/3）=16f（（x＋y）/2＋f（x）＋f（y）in the spirit of D. H. Hyers, S. M. Ulam, Th. M. Rassias and P. Gaevruta.展开更多
In this article, we study the existence, uniqueness, stability through continuous dependence on initial conditions and Hyers-Ulam-Rassias stability results for random impulsive fractional differential systems by relax...In this article, we study the existence, uniqueness, stability through continuous dependence on initial conditions and Hyers-Ulam-Rassias stability results for random impulsive fractional differential systems by relaxing the linear growth conditions. Finally, we give examples to illustrate its applications.展开更多
Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article give...Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article gives conditions for its Hyers-Ulam-Rassias stability. As a consequence, the authors obtain its Hyers-Ulam stability and prove that the equation has a unique multivalued solution near an approximate multivalued solution.展开更多
In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） i...In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.展开更多
In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to inv...In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.展开更多
In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are ob...In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.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
In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen...In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.展开更多
文摘Let n≥2 be an integer number. In this paper, we investigate the generalized Hyers Ulam- Rassias stability in Banach spaces and also Banach modules over a Banach algebra and a C＊-algebra and the stability using the alternative fixed point of an n-dimensional cubic functional equation in Banach spaces：f（2∑j=1^n-1 xj＋xn）＋f（2∑j=1^n-1 xj-xn）＋4∑j=1^n-1f（xj）=16f（∑j=1^n-1 xj）＋2∑j=1^n-1（f（xj＋xn）＋f（xj-xn）
基金Korea Research Foundation Grant KRF-2007-313-C00033
文摘In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation2f（x ＋ 2y） ＋ f（2x - y） = 5f（x ＋ y） ＋ 5f（x - y）＋ 15f（y）in the spirit of Hyers, Ulam, Rassias and Gavruta.
基金This work is supported by the Korea Research Foundation Grant funded by the Korea Government(MOEHRD)(KRF-2005-070-C00009)
文摘In this paper, we establish the general solution and the generalized Hyers-Ulam-Rassias stability problem for a cubic Jensen-type functional equation,4f（（3x＋y）/4）＋4f（（x＋3y）/4）=6f（（x＋y）/2）＋f（x）＋f（y）,9f（（2x＋y/3）＋9f（（x＋2y）/3）=16f（（x＋y）/2＋f（x）＋f（y）in the spirit of D. H. Hyers, S. M. Ulam, Th. M. Rassias and P. Gaevruta.
文摘In this article, we study the existence, uniqueness, stability through continuous dependence on initial conditions and Hyers-Ulam-Rassias stability results for random impulsive fractional differential systems by relaxing the linear growth conditions. Finally, we give examples to illustrate its applications.
文摘Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article gives conditions for its Hyers-Ulam-Rassias stability. As a consequence, the authors obtain its Hyers-Ulam stability and prove that the equation has a unique multivalued solution near an approximate multivalued solution.
文摘In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.
基金supported by the Daejin University grants in 2010
文摘In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.
文摘In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.
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.
文摘In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.
基金Supported by NSFC(10171014)Doctoral Programme Foundation of Institution of Higher Education and the Foundational of Fujian Educational Committee(JA02166)
