This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X,R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approxima...

When deriving the estimates on integral operators one often uses the Almost Orthogonality principle of M. Cotlar and E.M. Stein, first proved by M. Cotlar in [Cot55]. This result is classical; our excuse for formulating it once again is a need to have its weighted form which sometimes allows to reduce the number of integrations by parts in half (hereby weakening smoothness requirements), and al...

Classical results on weakly compactly generated (WCG) Banach spaces imply the existence of projectional resolutions of identity (PRI) and the existence of many projections on separable subspaces (SCP). We address the questions if these can be the only projections in a nonseparable WCG space, in the sense that there is a PRI (Pα : ω ≤ α ≤ λ) such that any projection is the sum of an operator in ...

employing the notions of the strong $l$-topology introduced by zhangand the $l$-frame introduced by yao  and the concept of $l$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf st$l$-top} of strong$l$-topological spaces, {bf s$l$-loc} of strict $l$-locales and{bf $l$-entopsys} of $l$-enriched topological systems. all of theseconcepts are ...

‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...

We shall define a Schrödinger operator for a one-dimensional simplicial complex (a graph) 1 Γ without ends (that is, at least two and only finitely many edges meet at any vertex), which acts on functions of vertices T or edges R: (Lψ) T = T ′ b T :T ′ ψ T ′ (V) for L 0 = ∂∂ * , b T :T ′ = 1, b T :T ′ = −m T , Here the coefficients are real, symmetric, and non-zero only for nearest neighbours T ...