Fixed set theorems with application to the fixed point theory

Abstract

Here, we show that continuous set-valued maps which are generalized set contraction on noncompact topological spaces have a maximal invariant (fixed) set. As an application, we prove the existence and uniqueness of endpoints for topological contraction mappings. Also, we present fractal set results for system of continuous set-valued maps on regular topological spaces. As application of our result, we show how some fixed point theorems can be established from these results. © 2016.