$beta$ -closed spaces and -$beta - theta$-subclosed graphs

Abstract

The purpose of this paper is to achieve various characterizations of $beta$ -closed spaces [2], specially, in terms of new types of graphs under the terminology -$beta$-$emptyset$subclosed graphs of functions and in terms of a generalized complete accumulation point. Apart from several properties, a sufficient condition for common fixed points of a family of functions having -$beta$-$emptyset$subclosed graphs is also given. AMS subject classifications: 54D20, 54D25, 54D30, 54C50.