Orlicz spaces and fixed point theory

his paper consists of mainly three topics on Orlicz spaces which are close to fixed point theory--a fundamental part of nonlinear functional analysis. The Orlicz space theory was established in early 30's and has been developed extensively in last 20 years. Many applications to differential and integral equations with kernels of nonpower types are the basic reason for the development of Orlicz spaces. Therefore, it is interesting to investigate the fixed point and related properties of Orlicz spaces. In chapter 2, we first study smoothness and differentiability of Orlicz spaces. Then we investigate the weak topology on abstract M spaces. We find a sufficient and necessary condition of weak convergence and weak compactness in abstract M spaces in terms of only the sequences and the subsets of abstract M spaces. This result is very useful since it is not easy to describe the bounded linear functionals on abstract M spaces. As an application, we obtain criteria of weak convergence and weak compactness in Orlicz spaces. In chapter 3, we first investigate the union and the intersection of Orlicz spaces. Compare with the union and the intersection of...