Convex ordered Gamma-semihypergroups associated to strongly regular relations

Abstract

In this study, we introduce and investigate the notion of convex ordered Gamma-semihypergroups associated to strongly regular relations. Afterwards, we prove that if sigma is a strongly regular relation on a convex ordered Gamma-semihypergroup, then the quotient set is an ordered Gamma-sigma-semigroup. Also, some results on the product of convex ordered Gamma-semihypergroups are given. As an application of the results of this paper, the corresponding results of ordered semihypergroups are also obtained by moderate modifications.