As an application of our previous paper, we give a sufficient condition that Brézis-Gallouët-Wainger type inequalities in higher order critical Sobolev spaces fails.

In this paper, an improvement and reverse of a strengthened Hardy-Knopp type inequality are obtained via log-convexity.

Observing that the logarithm of a product of two elliptic operators differs from the sum of the logarithms by a finite sum of operator brackets, we infer that regularised traces of this difference are local as finite sums of noncommutative residues. From an explicit local formula for such regularized traces, we derive an explicit local formula for the multiplicative anomaly of $\zeta$-determinants which sheds light on its locality and yields back previously known results.

In this paper, we investigate some new existence and uniqueness results for nonlinear fractional differential equations with four-point nonlocal integral boundary conditions by applying fixed point theorems.

In this paper, we introduce an iterative scheme for finding the common element of the set of fixed points of a countable family of nonexpansive mappings, the set of solutions of variational inequality for $\mu$-Lipschitzian, relaxed $(\lambda,\gamma)$-cocoercive mapping and the set of solutions of a generalized equilibrium problem. We show that the iterative sequence converges strongly to a common element of the three sets. Our results generalize many recent results, for example, the results of B. Ali [2].

We consider a singular differential-difference operator $\Lambda$ on $\R$ which generalizes the one-dimensional Dunkl operator. Using harmonic analysis associated with $\Lambda$ we define and study three types of generalized wavelet packets and the corresponding wavelet transforms. As an application, we introduce on $\R$ a new multiresolution analysis tied to $\Lambda$.

In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence

\begin{equation*} x_{n+1}=ax_{n}+\dfrac{bx_{n-l}+cx_{n-k}}{dx_{n-l}+ex_{n-k}},\;\;\;n=0,1,..., \end{equation*}

where the parameters $a,b,c,d\;$and$\;e\;$are positive real numbers and the initial conditions $x_{-k},x_{-k+1},...,x_{-l},x_{-l+1},...,x_{-1}$ and $x_{0}\;$are positive real numbers.

In this paper we study about some of the ergodicity properties of the Berezin transform $B$ on the $L^2$ space of the disk with respect to the invariant measure.