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 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
This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation x~?(t)-ax(t) = f(t), where a ∈ R^+. The main results can be regarded as a supplement of the stability results of the corres...This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation x~?(t)-ax(t) = f(t), where a ∈ R^+. The main results can be regarded as a supplement of the stability results of the corresponding homogeneous linear dynamic equation obtained by Anderson and Onitsuka(Anderson D R, Onitsuka M. Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales. Demonstratio Math., 2018, 51: 198–210).展开更多
We investigate the Hyers-Ulam stability(HUS)of certain second-order linear constant coefficient dynamic equations on time scales,building on recent results for first-order constant coefficient time-scale equations.In ...We investigate the Hyers-Ulam stability(HUS)of certain second-order linear constant coefficient dynamic equations on time scales,building on recent results for first-order constant coefficient time-scale equations.In particular,for the case where the roots of the characteristic equation are non-zero real numbers that are positively regressive on the time scale,we establish that the best HUS constant in this case is the reciprocal of the absolute product of these two roots.Conditions for instability are also given.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
基金Supported by the National Natural Science Foundation of China(11871064)the Graduate Research and Innovation Projects of Jiangsu Province(Yangzhou University)(XKYCX20_010)。
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 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This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation x~?(t)-ax(t) = f(t), where a ∈ R^+. The main results can be regarded as a supplement of the stability results of the corresponding homogeneous linear dynamic equation obtained by Anderson and Onitsuka(Anderson D R, Onitsuka M. Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales. Demonstratio Math., 2018, 51: 198–210).
基金supported by JSPS KAKENHI Grant Number JP20K03668。
文摘We investigate the Hyers-Ulam stability(HUS)of certain second-order linear constant coefficient dynamic equations on time scales,building on recent results for first-order constant coefficient time-scale equations.In particular,for the case where the roots of the characteristic equation are non-zero real numbers that are positively regressive on the time scale,we establish that the best HUS constant in this case is the reciprocal of the absolute product of these two roots.Conditions for instability are also given.
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.
