A fixed point approach to the hyers-ulam stability of a functional equation in various normed spaces
1 Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75914-353, Iran
2 Department of Mathematics, University of Ulsan, Ulsan 680-749, Korea
3 Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea
Fixed Point Theory and Applications 2011, 2011:67 doi:10.1186/1687-1812-2011-67Published: 25 October 2011
Using direct method, Kenary (Acta Universitatis Apulensis, to appear) proved the Hyers-Ulam stability of the following functional equation
in non-Archimedean normed spaces and in random normed spaces, where m, n are different integers greater than 1. In this article, using fixed point method, we prove the Hyers-Ulam stability of the above functional equation in various normed spaces.
2010 Mathematics Subject Classification: 39B52; 47H10; 47S40; 46S40; 30G06; 26E30; 46S10; 37H10; 47H40.