Contribution to study special kinds of hyperideals in ordered semihyperrings

In the present paper, we introduce the notion of k-hyperideals on ordered semihyperrings. Then, we investigate some fundamental properties of k-hyperideals of ordered semihyperrings. Indeed, we define (m, n)-hyperideals and (m, n)-bi-hyperideals in ordered semihyperrings and investigate some of their related properties. Moreover, we introduce and analyze the notion of prime (m, n)-bi-hyperideal of an ordered semihyperring.