In this paper, several fixed point theorems for T-contraction of two maps on cone metric spaces under normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.

A central idea of minimal model theory as formulated by Mori is to study algebraic varieties using convex geometry. The cone of curves of a projective variety is defined as the convex cone spanned by the numerical equivalence classes of algebraic curves; the dual cone is the cone of nef line bundles. For Fano varieties (varieties with ample anticanonical bundle), these cones are rational polyhe...

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in t...

In this paper, under a suitable regularity condition, we establish that a broad class of conic convex polynomial optimization problems, called conic sum-of-squares convex polynomial programs, exhibits exact conic programming relaxation, which can be solved by various numerical methods such as interior point methods. By considering a general convex cone-program, we give unified results that appl...

Consider a group G and an epimorphism u0 : G → Z inducing a splitting of G as a semidirect product ker(u0)oφ Z with ker(u0) a finitely generated free group and φ ∈ Out(ker(u0)) representable by an expanding irreducible train track map. Building on our earlier work [DKL], in which we realized G as π1(X) for an Eilenberg-Maclane 2–complex X equipped with a semiflow ψ, and inspired by McMullen’s T...

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

We study the nonlinear eigenproblem for monotone additively homogeneous maps f : Rn → Rn, and more generally, for monotone multiplicatively homogeneous maps on cones. When f is convex, monotone and additively homogeneous, we describe the nonlinear eigenspace of f using its subdifferential (or its tangent affine maps) [AG03]. This yields in particular an uniqueness result for the eigenvector of ...

Coconvex sets (complements in a convex cone of convex subsets coinciding with the cone far enough from its apex) appear in singularity theory (as Newton diagrams) and in commutative algebra. Such invariants of coconvex sets as volumes, mixed volumes, number of integer points, etc., play an important role. This paper aims at extending various results from the theory of convex bodies to the cocon...