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,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
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,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