Fixed point theorems for monotone multi-valued mappings in partially ordered metric spaces

Abstract

In this paper, we introduce two new types of monotone multi-valued mappings in partially ordered metric spaces and prove some fixed point theorems of those two types of mappings under some contraction conditions. Our main results extend many known results in the literature. Moreover, we also give an example which satisfies our main theorem but Nadler's theorem cannot be applied. © 2014 Tiammee and Suantai; licensee Springer.