Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti : K → E, i = 1, . . . ,r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed poin...

This paper considers advertising, collection and pricing decisions simultaneously for a closed-loop supplychain(CLSC) with one manufacturer(he) and two retailers(she). A multiplicatively separable new demand function is proposed which influenced by pricing and advertising. In this paper, three well-known scenarios in the game theory including the Nash, Stackelberg and Cooperative games are expl...

It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.

Some algorithms for nding common xed point of a family of mappings isconstructed. Indeed, let C be a nonempty closed convex subset of a uniformlyconvex Banach space X whose norm is Gateaux dierentiable and let {Tn} bea family of self-mappings on C such that the set of all common fixed pointsof {Tn} is nonempty. We construct a sequence {xn} generated by the hybridmethod and also we give the cond...

Let R be a real closed field and n ≥ 2. We prove that: (1) for every finite subset F of R, the semialgebraic set R \ F is a polynomial image of R; and (2) for any independent linear forms l1, . . . , lr of R , the semialgebraic set {l1 > 0, . . . , lr > 0} ⊂ R is a polynomial image of R.

‎This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...

The terminology and notation used here are introduced in the following articles: [10], [21], [17], [6], [20], [1], [9], [13], [2], [4], [18], [15], [5], [8], [11], [14], [12], [16], and [7]. For simplicity, we use the following convention: r, p, x denote real numbers, n denotes an element of N, A denotes a closed-interval subset of R, f , g denote partial functions from R to R, and Z denotes an...

Given polynomials h1, . . . , hr ∈ R[x1, . . . , xn], we study the complexity of the problem of representing polynomials in the form f = s0 + s1h1 + · · ·+ srhr (∗) with sums of squares si. Let M be the cone of all f which admit such a representation. The problem is said to be stable if there exists a function φ : N → N such that every f ∈ M has a representation (∗) with deg(si) ≤ φ(deg(f)). Th...

We investigate the question of whether or not the orbit of a point in A/Q, under the natural action of a subset Σ ⊆ Q, is dense in A/Q. We prove that if the set Σ is a multiplicative semigroup of Q× which contains at least two multiplicatively independent elements, one of which is an integer, then the orbit Σα of any point α with irrational real coordinate is dense.

We establish the following max-plus analogue of Minkowski’s theorem. Any point of a compact max-plus convex subset of (R∪{−∞})n can be written as the max-plus convex combination of at most n + 1 of the extreme points of this subset. We establish related results for closed max-plus convex cones and closed unbounded max-plus convex sets. In particular, we show that a closed max-plus convex set ca...