For a fixed nonnegative integer $m$, an analytic map $\varphi$ and function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued $f$, where $X$ Banach space. Some estimates norm of $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtain...

Abstract Let $\varphi _1,\ldots ,\varphi _r\in {\mathbb Z}[z_1,\ldots z_k]$ be integral linear combinations of elementary symmetric polynomials with $\text {deg}(\varphi _j)=k_j\ (1\le j\le r)$ , where $1\le k_1<k_2<\cdots <k_r=k$ . Subject to the condition $k_1+\cdots +k_r\ge \tfrac {1}{2}k(k-~1)+2$ we show that there is a paucity nondiagonal solutions Diophantine system _j({\mathbf x...

Recently, Zhang and Song [Q. Zhang, Y. Song, Fixed point theory forgeneralized $varphi$-weak contractions,Appl. Math. Lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. In this paper, we prove a common fixed point theorem fora family of compatible maps. In fact, a new generalization of Zhangand Song's theorem is given.

While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we present and study the logic rLTL which provides means to formally reason about both correctness design. Furthermore, identify large fragment of for verification problem can be efficiently solved, i.e., done by using an automaton, recognizing behaviors described form...

For a convex body $K$ in $\mathbb{R}^n$, we introduce and study the extremal general affine surface areas, defined by \[ {\rm IS}_{\varphi}(K):=\sup_{K^\prime\subset K}{\rm as}_{\varphi}(K),\quad os}_{\psi}(K):=\inf_{K^\prime\supset as}_{\psi}(K) \] where ${\rm as}_{\varphi}(K)$ as}_{\psi}(K)$ are $L_\varphi$ $L_\psi$ area of $K$, respectively. We prove that there exist bodies achieve supremum ...

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...