Bicontinuous biseparating operators on Orlicz spaces in the context of hypergroups

In this paper, first, we study bicontinuous biseparating left multipliers on Orlicz algebras in the context of a compact hypergroup and give some formula for them. Also, we assume that Φ is a ∆2-regular Young function with Φ ∈ ∆′ (globally) which is not equivalent to |x|² , and prove that if there is an isometry algebra isomorphism between convolution Orlicz algebras LΦ(G1) and LΦ(G2), then the underlying locally compact groups G1 and G2 are isomorphic.