Fixed point theorems of convex-power 1-set-contraction operators in Banach spaces
Department of Mathematics, Xuzhou Normal University, Xuzhou, China
Fixed Point Theory and Applications 2012, 2012:56 doi:10.1186/1687-1812-2012-56Published: 5 April 2012
In this article, we give the definition of a class of new operators, namely, convex-power 1-set-contraction operators in Banach spaces, and study the existence of fixed points of this class of operators. By using methods of approximation by operators, we obtain fixed point theorems of convex-power 1-set-contraction operators, which generalize fixed point theorems of 1-set-contraction operators in Banach spaces. By using the fixed point theorem, the existence of solutions of nonlinear Sturm-Liouville problems in Banach spaces is investigated under more general conditions than those used in former literatures.
Mathematics Subject Classification 2010: 47H10.