‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...

LetX be a Banach space with dualX∗, and letK be a nonempty subset ofX. A gauge function is a continuous strictly increasing function φ : R → R such that φ 0 0 and limt→∞φ t ∞. The duality mapping Jφ : X → X∗ associated with a gauge function φ is defined by Jφ x : {f ∈ X∗ : 〈x, f〉 ‖x‖‖f‖, ‖f‖ φ ‖x‖ }, x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. In the particular case φ t t, the ...

Given a finite or infinite set S and a positive integer k, a binary structure B of base S and of rank k is a function (S × S) \ {(x, x) : x ∈ S} −→ {0, . . . , k− 1}. A subset X of S is an interval of B if for a, b ∈ X and x ∈ S \X, B(a, x) = B(b, x) and B(x, a) = B(x, b). The family of intervals of B satisfies the following: ∅, B and {x}, where x ∈ B, are intervals of B; for every family F of ...

The main purpose of this manuscript is to prove a common fixed point theorem for two weakly compatible maps satisfying the following integral type contraction in \(G\)-metric space:\[\int^{G(\mathcal{F}x,\mathcal{F}y,\mathcal{F}z)}_0\varphi (t)dt\le \alpha \int^{L(x,y,z)}_0\varphi (t)dt,\] all \(x,y, z\in X\), where\begin{align*}L(x,y,z)&=\max\{G(gx, gy, gz), G(gx, \mathcal{F}x, \mathcal{F}...

Let Qd denote the hypercube of dimension d. Given d ≥ m, a spanning subgraph G of Qd is said to be (Qd, Qm)-saturated if it does not contain Qm as a subgraph but adding any edge of E(Qd) \E(G) creates a copy of Qm in G. Answering a question of Johnson and Pinto [27], we show that for every fixed m ≥ 2 the minimum number of edges in a (Qd, Qm)-saturated graph is Θ(2 d). We also study weak satura...

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...

A type of oscillation modeled on BMO is introduced to characterize norm compactness in L 1. This result is used to characterize the bounded linear operators from L 1 into a Banach space X that map weakly convergent sequences onto norm convergent sequences (i.e. are Dunford-Pettis). This characterization is used to study the geometry of Banach spaces X with the property that all bounded linear o...

In this paper, we introduce two concepts of weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in Banach spaces. Then we obtain some results of the solutions existence for a system of vector variational-like inequalities with weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in reflexive...

We establish that if F is a countable field of characteristic p, U is a unitary action of F` on a Hilbert space H , and P is an essential idempotent ultrafilter on F then for every polynomial r : F → F` with r(0) = 0 one has P-limg Ur(g)f = Prf weakly, where Pr is the projection onto the closed subspace Kr = { f ∈ H : {Ur(g)f}g∈F is precompact in the strong topology } . We then derive combinato...