Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces proved that a complete space, whose all closed bounded subsets are compact, mapping has fixed point. This article presents generalizations above results by omitting assumption compact.

The purpose of this paper is to study common fixed point theorems for six (four single-valued and two set-valued) mappings in fuzzy metric spaces. without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorem, we use a non compatible condition, that is, weak commutativity of type (Kh)in fuzzy metric spaces. We show that completeness of the whol...

For a tuple A = (A1, A2, ..., An) of elements in a unital Banach algebra B, its projective joint spectrum P (A) is the collection of z ∈ C such that A(z) = z1A1 +z2A2 + · · ·+znAn is not invertible. It is known that the B-valued 1-form ωA(z) = A−1(z)dA(z) contains much topological information about the joint resolvent set P (A). This paper defines Hermitian metric on P (A) through the B-valued ...

We study model theoretic properties of valued fields (equipped with a real-valued multiplicative valuation), viewed as metric structures in continuous first order logic. For technical reasons we prefer to consider not the valued field (K, |·|) directly, but rather the associated projective spaces KP, as bounded metric structures. We show that the class of (projective spaces over) metric valued ...