In this paper, we investigate the Hyers-Ulam stability of the following function equation 2f（2x ＋ y） ＋ 2f（2x - y） = 4f（x ＋ y） ＋ 4f（x - y） ＋ 4f（2x） ＋ f（2y） - Sf（x） - 8f（y） in quasi-β-normed spaces.
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is...In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.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
The primary varicella-zoster virus(VzV)infection that causes chickenpox(also known as varicella),spreads quickly among people and,in severe circumstances,can cause to fever and encephalitis.In this paper,the Mittag-Le...The primary varicella-zoster virus(VzV)infection that causes chickenpox(also known as varicella),spreads quickly among people and,in severe circumstances,can cause to fever and encephalitis.In this paper,the Mittag-Leffler fractional operator is used to examine the mathematical representation of the vzV.Five fractional-order differential equations are created in terms of the disease's dynamical analysis such as S:Susceptible,V:Vaccinated,E:Exposed,I:Infectious and R:Recovered.We derive the existence criterion,positive solution,Hyers-Ulam stability,and boundedness of results in order to examine the suggested fractional-order model's wellposedness.Finally,some numerical examples for the VzV model of various fractional orders are shown with the aid of the generalized Adams-Bashforth-Moulton approach to show the viability of the obtained results.展开更多
Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk...Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.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
In this paper,using the fixed-point and direct methods,we prove the HyersUlam stability of the following m-Appolonius type functional equation：∑mi=1 f（z-xi）=mf（z-1/m2∑mi=1xi）-1/m∑1≤i〈j≤mf（xi＋xj）,where m ...In this paper,using the fixed-point and direct methods,we prove the HyersUlam stability of the following m-Appolonius type functional equation：∑mi=1 f（z-xi）=mf（z-1/m2∑mi=1xi）-1/m∑1≤i〈j≤mf（xi＋xj）,where m is a natural number greater than 1,in random normed spaces. 更多还原展开更多
The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of ...The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.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
In this paper,we obtain the general solution and stability of the Jensen-cubic functional equation f（（x1＋x2）/2,2y1＋y2）＋f（（x1＋x2）/2,2（y1-y2）） = f（x1,y1 ＋y2）＋f（x1,y1-y2）＋6f（x1,y1＋ f（x2,y1y2）＋f...In this paper,we obtain the general solution and stability of the Jensen-cubic functional equation f（（x1＋x2）/2,2y1＋y2）＋f（（x1＋x2）/2,2（y1-y2）） = f（x1,y1 ＋y2）＋f（x1,y1-y2）＋6f（x1,y1＋ f（x2,y1y2）＋f（x2,y1-y2）＋6f（x2,y1）.展开更多
Let n ≥ 2 be an integer. In this paper, we investigate the generalized Hyers-Ulam stability problem for the following functional equation f（n-1∑j=1 xj＋2xn）＋f（n-1∑j=1 xj-2xn）＋8 n-1∑j=1f（xj）=2f（n-1∑j=1 xj...Let n ≥ 2 be an integer. In this paper, we investigate the generalized Hyers-Ulam stability problem for the following functional equation f（n-1∑j=1 xj＋2xn）＋f（n-1∑j=1 xj-2xn）＋8 n-1∑j=1f（xj）=2f（n-1∑j=1 xj） ＋4 n-1∑j=1[f（xj＋xn）＋f（xj-xn）] which contains as solutions cubic, quadratic or additive mappings.展开更多
In this paper, we introduce an additive functional inequality and a quadratic functional inequality in normed spaces, and prove the Hyers-Ulam stability of the functional inequalities in Banach spaces. Furthermore, we...In this paper, we introduce an additive functional inequality and a quadratic functional inequality in normed spaces, and prove the Hyers-Ulam stability of the functional inequalities in Banach spaces. Furthermore, we introduce an additive functional inequality and a quadratic functional inequality in non-Archimedean normed spaces, and prove the Hyers-Ulam stability of the functional inequalities in non-Archimedean Banach spaces.展开更多
Using the fixed point method, we prove the Hyers Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces.
Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional e...Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.展开更多
In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hye...In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hyers-Ulam stability of the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces and prove the Hyers-Ulam stability of quadratic p-functional equations associated with the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces.展开更多
We consider the Hyers-Ulam stability problem of the generalized quadratic functional equationuoA＋voB-2woP1 - 2ko P2 =0, which is a distributional version of the classical generalized quadratic functional equation f（...We consider the Hyers-Ulam stability problem of the generalized quadratic functional equationuoA＋voB-2woP1 - 2ko P2 =0, which is a distributional version of the classical generalized quadratic functional equation f（x＋y）＋g（x - y） - 2h（x） - 2k（y）=0展开更多
In this paper, we study the boundary value problem for an impulsive fractional <i><span style="font-family:Verdana;"><i>q</i></span></i><span style="font-family:Ve...In this paper, we study the boundary value problem for an impulsive fractional <i><span style="font-family:Verdana;"><i>q</i></span></i><span style="font-family:Verdana;">-difference equation. Based on Banach’s contraction mapping principle, the existence and Hyers-Ulam stability of solutions for the equation which we considered are obtained. At last, an illustrative example is given for the main result.</span>展开更多
The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of no...The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.展开更多
Recently, Popa and Rata [27, 28] have shown the （in）stability of some classical operators defined on [0, 1] and found best constant when the positive linear operators are stable in the sense of Hyers-Ularn. In this ...Recently, Popa and Rata [27, 28] have shown the （in）stability of some classical operators defined on [0, 1] and found best constant when the positive linear operators are stable in the sense of Hyers-Ularn. In this paper we show Hyers-Ulam （in）stability of complex Bernstein-Schurer operators, complex Kantrovich-Schurer operators and Lorentz operators on compact disk. In the case when the operator is stable in the sense of Hyers and Ulam, we find the infimum of Hyers-Ulam stability constants for respective operators.展开更多
In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14...In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.展开更多
基金Supported by National Science Foundation of China (Grant Nos. 10626031 and 10971117) the Scientific Research Project of the Department of Education of Shandong Province (Grant No. J08LI15)
文摘In this paper, we investigate the Hyers-Ulam stability of the following function equation 2f（2x ＋ y） ＋ 2f（2x - y） = 4f（x ＋ y） ＋ 4f（x - y） ＋ 4f（2x） ＋ f（2y） - Sf（x） - 8f（y） in quasi-β-normed spaces.
文摘In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.
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The primary varicella-zoster virus(VzV)infection that causes chickenpox(also known as varicella),spreads quickly among people and,in severe circumstances,can cause to fever and encephalitis.In this paper,the Mittag-Leffler fractional operator is used to examine the mathematical representation of the vzV.Five fractional-order differential equations are created in terms of the disease's dynamical analysis such as S:Susceptible,V:Vaccinated,E:Exposed,I:Infectious and R:Recovered.We derive the existence criterion,positive solution,Hyers-Ulam stability,and boundedness of results in order to examine the suggested fractional-order model's wellposedness.Finally,some numerical examples for the VzV model of various fractional orders are shown with the aid of the generalized Adams-Bashforth-Moulton approach to show the viability of the obtained results.
文摘Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.
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In this paper,using the fixed-point and direct methods,we prove the HyersUlam stability of the following m-Appolonius type functional equation：∑mi=1 f（z-xi）=mf（z-1/m2∑mi=1xi）-1/m∑1≤i〈j≤mf（xi＋xj）,where m is a natural number greater than 1,in random normed spaces. 更多还原
文摘The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.
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 obtain the general solution and stability of the Jensen-cubic functional equation f（（x1＋x2）/2,2y1＋y2）＋f（（x1＋x2）/2,2（y1-y2）） = f（x1,y1 ＋y2）＋f（x1,y1-y2）＋6f（x1,y1＋ f（x2,y1y2）＋f（x2,y1-y2）＋6f（x2,y1）.
基金supported by research fund of Chungnam National University in 2008
文摘Let n ≥ 2 be an integer. In this paper, we investigate the generalized Hyers-Ulam stability problem for the following functional equation f（n-1∑j=1 xj＋2xn）＋f（n-1∑j=1 xj-2xn）＋8 n-1∑j=1f（xj）=2f（n-1∑j=1 xj） ＋4 n-1∑j=1[f（xj＋xn）＋f（xj-xn）] which contains as solutions cubic, quadratic or additive mappings.
基金Supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(Grant No.NRF-2012R1A1A2004299)
文摘In this paper, we introduce an additive functional inequality and a quadratic functional inequality in normed spaces, and prove the Hyers-Ulam stability of the functional inequalities in Banach spaces. Furthermore, we introduce an additive functional inequality and a quadratic functional inequality in non-Archimedean normed spaces, and prove the Hyers-Ulam stability of the functional inequalities in non-Archimedean Banach spaces.
基金supported by Basic Science Research Program through National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (Grant No. NRF-2012R1A1A2004299)
文摘Using the fixed point method, we prove the Hyers Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces.
文摘Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.
基金supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(NRF-2012R1A1A2004299)
文摘In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hyers-Ulam stability of the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces and prove the Hyers-Ulam stability of quadratic p-functional equations associated with the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces.
基金Supported by the Korean Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (Grant No. KRF-2007-521-C00016)
文摘We consider the Hyers-Ulam stability problem of the generalized quadratic functional equationuoA＋voB-2woP1 - 2ko P2 =0, which is a distributional version of the classical generalized quadratic functional equation f（x＋y）＋g（x - y） - 2h（x） - 2k（y）=0
文摘In this paper, we study the boundary value problem for an impulsive fractional <i><span style="font-family:Verdana;"><i>q</i></span></i><span style="font-family:Verdana;">-difference equation. Based on Banach’s contraction mapping principle, the existence and Hyers-Ulam stability of solutions for the equation which we considered are obtained. At last, an illustrative example is given for the main result.</span>
基金supported by the Natural Science Foundation of Yibin University(No.2009Z03)
文摘The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.
文摘Recently, Popa and Rata [27, 28] have shown the （in）stability of some classical operators defined on [0, 1] and found best constant when the positive linear operators are stable in the sense of Hyers-Ularn. In this paper we show Hyers-Ulam （in）stability of complex Bernstein-Schurer operators, complex Kantrovich-Schurer operators and Lorentz operators on compact disk. In the case when the operator is stable in the sense of Hyers and Ulam, we find the infimum of Hyers-Ulam stability constants for respective operators.
文摘In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.
