The main purpose of this paper is to study the non-emptiness and $\text{H}$-closeness of inverse limits of $\text{H}$-closed spaces.

In this paper, we introduce and study a class ${\tilde{Q}}_k(\alpha ,\beta ,\rho ,\gamma )$ of analytic functions in the unit disc. This class generalizes the concept of quasiconvexity. Inclusion results, distortion theorem and some other properties of this class are investigated.

We present the results of numerical experiments in connection with the Riesz and the Hardy-Littlewood criteria for the truth of the Riemann Hypothesis (RH). The coefficients $c_k$ of the Pochhammer expansion for the reciprocal of the Riemann Zeta function depend in our model on two parameters. The “critical functions” $c_k{k}^a$ (where $a$ is some constant), whose behaviour is concerned with the possible truth of the RH, are analysed at relatively large values of $k$. Some cases are numerically investigated up to larger values of $k$, i.e. $k={10}^9$ and more.

The $c_k$ we obtain in such a region have an oscillatory behaviour, which we call the Riesz and the Hardy-Littlewood wave. A special case is then studied numerically in some range of the critical strip. The numerical results give some evidence that the critical function is bounded for and such an “evidence” is stronger in the region where the wave seems to decay slowly. This give further support in favour of the absence of zeros of the Riemann Zeta function in some regions of the critical strip () and a (weaker) support in the direction to believe that the RH may be true ().

The amplitudes and the wavelength of the wave obtained by our numerical treatment are then compared with those formulated by Baez-Duarte in his analytical approach. The agreement is satisfactory.

Finally for another special case we found that the wave appears to be bounded even though one parameter in our model grows to infinity. Our analysis suggests that RH may barely be true and it is argued that an absolute bound on the amplitudes of the waves in all cases, should be given by $|\frac{1}{\zeta (\frac{1}{2}+ϵ)}-1|$, with $ϵ$ arbitrarily small positive, i.e. equal to $1.68477\dots$.

In this paper, we establish some new oscillation criteria for nonautonomous second order neutral delay dynamic equation with several delays

$${(x(t)-r(t)x(\tau (t)))}^{△△}+H(t,x(h(t)))+G(t,x(g(t)))=0,$$

on a time scale $\mathbb{T}$. The results not only can be applied on neutral differential equations when $\mathbb{T}=ℝ$, neutral delay difference equations when $\mathbb{T}=\mathbb{N}$ and for neutral delay $q-$ difference equations when $\mathbb{T}=q^{\mathbb{N}}$ for , but also improved most previous results.

We prove existence results for boundary value problems for second order convex and nonconvex differential inclusions with integral boundary conditions. The proofs use nonlinear alternatives of Leray-Schauder type and a selection theorem due to Bressan and Colombo.

A general method“weighted method” will be presented which allows to extend various inequalities for one function case to inequalities for multifunctional case in the unit disk, unit ball and polydisk.

This paper concerns the study of the numerical approximation for the following initial-boundary value problem:

where , and . We show that under some conditions, the solution of a semidiscrete form of $(P)$ either decays uniformly to zero or blows up in a finite time. When the blow-up occurs, we estimate the semidiscrete blow-up time and prove that under some assumptions, the semidiscrete blow-up time converges to the real one when the mesh size goes to zero. When the semidiscrete solution goes to zero as $t$ goes to infinity, we give its asymptotic behavior. Finally, we give some numerical experiments to illustrate our analysis.

In this paper, we suggest and analyze a new extragradient method for finding a common element of the set of solutions of an equilibrium problem, the set of fixed points of a nonexpansive mapping and the set of solutions of some variational inequality. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets. Our result includes the main result of Bnouhachem, Noor and Hao [A. Bnouhachem, M.A. Noor and Z. Hao, Some new extragradient methods for variational inequalities, Nonlinear Analysis (2008), doi: 10.1016/j.na.2008.02.014] as a special case.