We prove the following criterium of weak compactness in the dual of a JB*-triple: a bounded set K in the dual of a JB*-triple E is not relatively weakly compact if and only if there exist a sequence of pairwise orthogonal elements (an) in the closed unit ball of E, a sequence (φn) in K , and θ > 0 satisfying that |φn(an)| > θ for all n ∈ N. This solves a question stimulated by the main result i...

the aim of the present paper is to define and study (ic)$lm$-fuzzytopological spaces, a generalization of (weakly) induced $lm$-fuzzytopological spaces. we discuss the basic properties of(ic)$lm$-fuzzy topological spaces, and introduce the notions ofinterior (ic)-fication and exterior (ic)-fication of $lm$-fuzzytopologies and prove that {bf iclm-ftop} (the category of(ic)$lm$-fuzzy topological ...

In several e-commerce applications, non-truthful auctions have been preferred over truthful weakly dominant strategy ones partly because of their simplicity and scalability. Although nontruthful auctions can have weaker incentive constraints than truthful ones, the question of how much more revenue they can generate than truthful auctions is not well understood. We study this question for natur...

In the paper we provide construction of a coincidence degree being homotopy invariant detecting existence solutions equations or inclusions form $Ax\in F(x)$, $x\in U$, where $A\colon D(A)\multimap E$ is an $m$-accretive operator in Banach space $ E$, $F\colon K\multimap weakly upper semicontinuous set-valued map constrained to open subset $U$ closed set $K\subset E$. Two different approaches w...

Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F (T ) the set of fixed points of T . Kirk [21] proved that F (T ) is nonempty in the case that C is weakly compact and has normal structure. See also [3, 4, 5, 14] and others. If C is weakly compact and E has the Opial property, then C has n...

Abstract The paper investigates the algebraic properties of weakly inverse-closed complex Banach function algebras generated by functions bounded variation on a finite interval. It is proved that such have Bass stable rank 1 and are projective-free if they do not contain nontrivial idempotents. These derived from new result vanishing second Čech cohomology group polynomially convex hull continu...