Davvaz (2008) introduced the concept of set-valued homomorphism andT-rough sets in a group. In this paper, we consider the set-valued homomorphismTonΓ-semihypergroupHto interpret the lower and upper approximations. We study the roughness of(m,n)bi-Γ-hyperideals and(m,n)quasi-Γ-hyperideals in terms of set-valued homomorphisms, which are extended notions of(m,n)bi-Γ-hyperideals and(m,n)quasi-Γ-hyperideals ofΓ-semihypergroups.
The object of this paper is to emphasize the role of 'common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 24(2) (2008]. In the process, we also derive a fixed point result satisfying φ-contractive condition.
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