‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some‎ ‎useful theorems‎. ‎Our results on multiplicative metric space improve and modify‎ ‎s...

We consider the completely positive map on the Toeplitz operator system given by conjugation by a composition operator; that is, we analyze operators of the form C∗ φTfCφ We prove that every such operator is weakly asymptotically Toeplitz, and compute its asymptotic symbol in terms of the Aleksandrov-Clark measures for φ. When φ is an inner function, this operator is Toeplitz, and we show under...

We prove existence and regularity of entire solutions to MongeAmpère equations invariant under an irreducible action of a compact Lie group. We consider Monge-Ampère equations of the form f(∇φ) detDijφ = g(x) (0.1) where f and g are nonnegative measurable functions on R. We recall first the concept of a weak solution of (0.1). Let φ be a convex function. Then ∇φ is a well-defined multi-valued m...

Abstract In this paper, using the notion of w -distance in metric spaces, we introduce two types nonlinear contractions, $(\iota ,\psi ,\varphi ,\phi ,p)$ ( ι , ψ φ ϕ p ) and rational- , \var...

Letting π : X → Y be a one-block factor map and Φ be an almostadditive potential function on X, we prove that if π has diamond, then the pressure P (X,Φ) is strictly larger than P (Y, πΦ). Furthermore, if we define the ratio ρ(Φ) = P (X,Φ)/P (Y, πΦ), then ρ(Φ) > 1 and it can be proved that there exists a family of pairs {(πi,Xi)}ki=1 such that πi : Xi → Y is a factor map between Xi and Y , Xi ⊆...

In this paper, we prove the first conjecture of Bar-Natan, Garo-ufalidis, and Khovanov's on the Khovanov's invariants for alternating knots. 1. The map Φ The first conjecture states that there is an almost pairing of the cohomology groups of degree difference (1,4), so it is natural to think of a map of degree (1,4) on the cohomology groups. On chain level, the map Φ is defined in the same fash...

In this paper, we prove the Spanne-Guliyev type boundedness of the generalized fractional integral operator Iρ from the vanishing generalized local Morrey spaces V LM {x0} p,φ1 to V LM {x0} q,φ2 , 1 < p < q < ∞, and from the space V LM {x0} 1,φ1 to the weak space VWLM {x0} q,φ2 , 1 < q < ∞. We also prove the Adams-Guliyev type boundedness of the operator Iρ from the vanishing generalized Morrey...

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in [16], [8], [6], [7]. We then apply the equation to show that the generalized Chen’s conjecture is true for totally umbilical biharmonic hypersurfaces in an Einstein space, and construct a (2-p...

Mitogen-activated protein (MAP) kinases regulate smooth muscle cell contraction. Hypoxia contracts pulmonary arteries by mechanisms that are incompletely understood. We hypothesized that hypoxic contraction of pulmonary arteries involves activation of the MAP kinases. To test this hypothesis, we studied the effects of SB-202190, a p38 MAP kinase inhibitor, PD-98059 and UO-126, two structurally ...