We show that an example of a nonhyperreflexive CSL algebra recently constructed by Davidson and Power is a special case of a general and natural reflexive subspace construction. Completely different techniques of proof are needed because of absence of symmetry. It is proven that if y and ¿T are reflexive proper linear subspaces of operators acting on a separable Hubert space, then the hyperrefl...

This paper is concerned with the study of solution existence of variational inequalities and generalized variational inequalities in reflexive Banach spaces with pseudomonotone operators in the sense of H. Brézis. The obtained results covers some preceding results in [4], [11] and [14].

Let X be a separable infinite-dimensional Banach space, and let A be a set of normalized sequences in X. We can consider a two-player game in X each move of which consists of player S (subspace chooser) selecting some element Y from the set cof(X) of finite-codimensional subspaces of X, and P (point chooser) responding by selecting a vector y from the unit sphere SY of Y . The game, which we sh...

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.

In this paper, we introduce the notion of extended relaxed -monotonicity. We obtain existence solution of the generalized mixed equilibrium problems in reflexive Banach spaces with extended relaxed -monotonicity by using the KKM technique. Our results extend and improve the corresponding results in the existing literature.

By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.

Suppose somenon-degenerate preferencesR, with strict part P , over risky outcomes satisfy Independence. Then, when they satisfy any two of the following axioms, they satisfy the third. Herstein–Milnor: for all lotteries p, q, r , the set of a’s for which ap + (1 − a)qRr is closed. Archimedean: for all p, q, r there exists a > 0 such that if pPq, then ap + (1 − a)rPq. Complete: for all p, q, eit...

Standard Dutch and German have two reflexive forms: a weak form (zich in Dutch and sich in German) and a strong form (zichzelf in Dutch and sich selbst in German). The choice between the two reflexive forms in Dutch has been explained by the selectional restrictions of the verb, distinguishing between three verb classes: inherently reflexive verbs, accidentally reflexive verbs and transitive ve...

ing from the embeddability relation between order types, define a quasi-order to be a reflexive, transitive relation. Throughout this paper, the letters Q and R will range over quasi-ordered sets and classes. Various quasi-ordered spaces will be defined; in each case we will use the symbol < (perhaps with subscripts) to denote the quasi-order under consideration. If q1, q2 E Q, write ql < q2 to...