in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed linear space, thatis, the mazur-ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

In this article, the open problem of finding exact value norm Hilbert matrix operator on weighted Bergman spaces \(A^p_\alpha\) is adressed. The was conjectured to be \(\frac{\pi}{\sin \frac{(2+\alpha)\pi}{p}}\) by Karapetrovic. We obtain a complete solution conjecture for \(\alpha > 0\) and \(2+\alpha+\sqrt{\alpha^2+\frac{7}{2}\alpha+3} \le p < 2(2+\alpha)\) partial \(2+2\alpha 2+\alpha+\sqrt{...

For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$,  we definea  subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In  the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative  $mathrm{T}...

Recently, in paper [14], we have introduced the following deformed $(\alpha, \beta)$-metric: $$ F_{\epsilon}(\alpha,\beta)=\frac{\beta^{2}+\alpha^{2}(a+1)}{\alpha}+\epsilon\beta where $\alpha=\sqrt{a_{ij}y^{i}y^{j}}$ is a Riemannian metric; $\beta=b_{i}y^{i}$ 1-form, $\left|\epsilon\right|&amp;lt;2\sqrt{a+1}$ real parameter and $a\in \left(\frac{1}{4},+\infty\right)$ positive scalar. The aim of...

In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%-normed linear space or $Im (X)$ is a fuzzy $2$-normed linear space, thatis, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

In this note, we prove weighted resolvent estimates for the semiclassical Schrodinger operator $-h^2 \Delta + V(x) : L^2(\mathbb{R}^n) \to L^2(\mathbb{R}^n)$, $n \neq 2$. The potential $V$ is real-valued, and assumed to either decay at infinity or obey a radial $\alpha$-Holder continuity condition, $0\leq \alpha \leq 1$, with sufficient of local $C^\alpha$ norm toward infinity. Note, however, t...

We consider the dynamics of even solutions one-dimensional nonlinear Klein-Gordon equation $\partial_t^2 \phi - \partial_x^2 + |\phi|^{2\alpha} =0$ for $\alpha>1$, in vicinity unstable soliton $Q$. Our main result is that stability energy space $H^1(\mathbb R)\times L^2(\mathbb R)$ implies asymptotic a local norm. In particular, there exists Lipschitz graph initial data leading to stable and as...

in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.

We investigate the permissible growth rates of functions that are distributionally chaotic with respect to differentiation operators. improve on known estimates for $D$-distributionally entire functions, where is in terms average $L^p$-norms spheres radius $r>0$ as $r \to \infty$, $1 \leq p \infty$. compute $\partial/ \partial x_k$-distributionally harmonic $L^2$-norm also calculate sup-norm ca...