Solutions of a variational inequality problemdefined by a closed and convex set and a mapping are found by imposing conditions for the monotone convergence with respect to a cone of the Picard iteration corresponding to the composition of the projection onto the defining closed and convex set and the difference in the identity mapping and the defining mapping. One of these conditions is the iso...

Abstract In this paper, the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced. The fixed point theorems satisfying contractive conditions are obtained, without appealing to completeness of X or normality cone. continuity mapping relaxed. Furthermore, we prove that necessary if has a . These results greatly generalize several well-known comparable liter...

Let X be a nonempty, compact, convex set in R and let f be an upper semicontinuous mapping from X to the collection of nonempty, compact, convex subsets of R. It is well known that such a mapping has a stationary point on X; i.e., there exists a point X such that its image under f has a nonempty intersection with the normal cone of X at the point. In the case where, for every point in X, it hol...

In this paper, we introduce the class of ideals with $(d_1,ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.

In order to gain deeper understanding of pure-spinor-based formalisms of superstring, an explicit similarity transformation is constructed which provides operator mapping between the light-cone Green-Schwarz (LCGS) formalism and the extended pure spinor (EPS) formalism, a recently proposed generalization of the Berkovits’ formalism in an enlarged space. By applying a systematic procedure develo...

Let P be a cone in a Hilbert space H, A : P → 2 be an accretive mapping (equivalently, −A be a dissipative mapping) and T : P → P be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type −A+T are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equati...

Let X be a reduced closed subscheme in P. As a slight generalization of property Np due to Green-Lazarsfeld, we can say that X satisfies property N2,p scheme-theoretically if there is an ideal I generating the ideal sheaf IX/Pn such that I is generated by quadrics and there are only linear syzygies up to p-th step (cf. [9], [10], [21] ). Recently, many algebraic and geometric results have been ...

The presence of geometric details on object surfaces dramatically changes the way light interacts with these surfaces. Although synthesizing realistic pictures requires simulating this interaction as faithfully as possible, explicitly modeling all the small details tends to be impractical. To address these issues, an image-based technique called relief mapping has recently been introduced for a...

We study infinite dimensional optimization problems where the constraint mapping is given as the sum of a smooth function and a generalized polyhedral multifunction, e.g. the normal cone mapping of a convex polyhedral set. By using advanced techniques of variational analysis we obtain first-order and second-order characterizations, both necessary and sufficient, for directional metric subregula...