New Fixed Point Tools in Non-metrizable Spaces

Abstract

Abstract. The aim of this paper is to provide some sufficient conditions under which a self-mapping T defined on a non-empty set X endowed with some convergence property is a Picard operator. A relevant example showing that such a mapping T on a non-metrizable space is a Picard operator is given. Our results can be used to obtain some known fixed point theorems on generalized metric spaces.Mathematics Subject Classification. 47H09, 47H10.