On the stability of set-valued functional equations with the fixed point alternative
1 Department of Mathematics, College of Science, Yasouj University, Yasouj 75914-353, Iran
2 Department of Mathematics, Islamic Azad University, Bushehr Branch, Bushehr, Iran
3 Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea
Fixed Point Theory and Applications 2012, 2012:81 doi:10.1186/1687-1812-2012-81Published: 10 May 2012
Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic set-valued functional equation, a generalized quadratic set-valued functional equation and a Jensen type cubic set-valued functional equation.
Mathematics Subject Classification 2010: 47H10; 54C60; 39B52; 47H04; 91B44.