We introduce a vector-valued version of uniform algebra, called the function space over algebra. The diameter two properties algebra on an infinite compact Hausdorff are investigated. Every nonempty relatively weakly open subset unit ball $$A(K, (X, \tau ))$$ dimensional has two, where $$\tau $$ is locally convex topology Banach X compatible to dual pair. Under assumption equipped with norm bei...

It is known that there are several approaches to define a Sobolev class for Banach valued functions. We compare the usual definition via weak derivatives with Reshetnyak–Sobolev space and Newtonian space; in particular, we provide sufficient conditions when all three agree. Also, revise difference quotient criterion property of Lipschitz mapping preserve it acting as superposition operator.

In this paper, we enlarge the language of triangle algebra by addinga unary operation that describes properties of a state. Thesestructure algebras are called state triangle algebra. The vitalproperties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and givesome examples and properties of them are given. ...

Let Kn be the Lorentz/second-order cone in IR. For any function f from IR to IR, one can define a corresponding vector-valued function f soc (x) on IR by applying f to the spectral values of the spectral decomposition of x ∈ IR with respect to Kn. It was shown by J.-S. Chen, X. Chen and P. Tseng that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity,...