Fixed point theorems and stability of fixed point sets of multivalued mappings

Abstract

In this paper, we prove new fixed point theorems of multivalued mappings in partially ordered metric spaces using newly reformulated pre-order relations. As consequence, we derive fixed point theorems for single valued mappings given by Nieto and Rodriguez-Lopez [11], [12]. We also establish some results on the stability of fixed point sets of multivalued mappings in partially ordered metric spaces. General illustrative examples are also given. Essential to our results are the pre-order relations <1,<2,<3defined in [3], and newly reformulated pre-order relations namely <4,<5,<6, which are obtained by imposing a distance condition to comparable elements of two non-empty, closed and bounded sets.