In this paper we introduce a definition of gradation of continuity ingraded fuzzy topological spaces and study its various characteristic properties.The impact of the grade of continuity of mappings over the N-compactnessgrade is examined. Concept of gradation is also introduced in openness, closed-ness, homeomorphic properties of mappings and T2 separation axiom. Effectof the grades interrelat...

Let X be a Banach space and T bounded linear operator acting in lp(ℤc,X), 1 ≤ p ∞. The is called locally nuclear if it can represented the form $${(Tx)_k} = \sum\limits_{m \in {\mathbb{Z}^c}} {{b_{km}}} {x_{k - m}},\quad k {\mathbb{Z}^c},$$ where bkm: → are nuclear, $${\left\| \right\|_{{\mathfrak{S}_1}}} \le {\beta _m},\quad k,m $$\left\|\cdot\right\|{_{{\mathfrak{S}_1}}}$$ norm, β ∈ l1(ℤc,ℂ) ...

We introduce a new type of the system of generalized strong vector quasiequilibrium problems with set-valued mappings in real locally convex Hausdorff topological vector spaces. We establish an existence theorem by using Kakutani-Fan-Glicksberg fixed-point theorem and discuss the closedness of strong solution set for the system of generalized strong vector quasiequilibrium problem. The results ...

Received: 27 March 2012; Accepted: 25 July 2012. Published online: XX July. 2012 Abstract: In this paper, we prove a common fixed point theorem for occasionally weakly compatible mappings on fuzzy metric space satisfying an implicit relation. Our result never requires the completeness (or closedness) of the whole space (or subspaces), containment of ranges amongst involved mappings and continui...

We study closedness properties of internal relations in finitely complete categories, which leads to developing a unified approach to: Mal’tsev categories, in the sense of A.Carboni, J. Lambek and M.C.Pedicchio, that generalize Mal’tsev varieties of universal algebras; unital categories, in the sense of D.Bourn, that generalize pointed Jónsson-Tarski varieties; and subtractive categories, intro...