Soft Quasilinear Spaces and Soft Normed Quasilinear Spaces

Soft linear operators in soft normed linear spaces

In the present paper an idea of soft linear operator over soft linear spaces has been introduced and some basic properties of such operators are studied. Spaces of continuous soft linear operators are investigated and lastly the inverse of a soft linear operator is defined and its properties are studied. 2010 AMS Classification: 03E72, 08A72

Soft Connected Spaces and Soft Paracompact Spaces

Quasilinear evolutionary equations and continuous interpolation spaces

In this paper we analyze the abstract parabolic evolutionary equations Dt ðu xÞ þ AðuÞu 1⁄4 f ðuÞ þ hðtÞ; uð0Þ 1⁄4 x; in continuous interpolation spaces allowing a singularity as tk0: Here Dt denotes the timederivative of order aAð0; 2Þ: We first give a treatment of fractional derivatives in the spaces Lðð0;TÞ;XÞ and then consider these derivatives in spaces of continuous functions having (at m...

On exponentiable soft topological spaces

An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable  spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalizati...

Quasilinear Degenerate Evolution Equations in Banach Spaces

The quasilinear degenerate evolution equation of parabolic type d(Mv) dt + L(Mv)v = F (Mv), 0 < t ≤ T considered in a Banach space X is written, putting Mv = u, in the form du dt + A(u)u 3 F (u), 0 < t ≤ T , where A(u) = L(u)M−1 are multivalued linear operators in X for u ∈ K, K being a bounded ball ‖u‖Z < R in another Banach space Z continuously embedded in X. Existence and uniqueness of the l...