‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...

‎Complex-valued harmonic functions that are univalent and‎ ‎sense-preserving in the open unit disk $U$ can be written as form‎ ‎$f =h+bar{g}$‎, ‎where $h$ and $g$ are analytic in $U$‎. ‎In this paper‎, ‎we introduce the class $S_H^1(beta)$‎, ‎where $1<betaleq 2$‎, ‎and‎ ‎consisting of harmonic univalent function $f = h+bar{g}$‎, ‎where $h$ and $g$ are in the form‎ ‎$h(z) = z+sumlimits_{n=2}^inf...

we show that the variational inequality $vi(c,a)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-lipschitzian mapping $a: cto h$ with $r>gamma mu^2$, where$c$ is a nonempty closed convex subset of a hilbert space $h$. fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...

For every Hausdorff space X the space XΘ is introduced. If X is H-closed, then XΘ is a quasy-compact T1-space. If f : X → Y is a mapping, then there exists the mapping fΘ : XΘ → YΘ. We say that a mapping f : X → Y is Θ-closed if fΘ is a closed mapping. If X and Y are H-closed and if f : X → Y is a HJ-mapping, then fΘ is Θ-closed. Let X = {Xa, pab, A} be an inverse system of H-closed spaces Xa a...

We use topological consequences of {\sf PFA}, MA$_{\omega_1}$(S)[S]} and PFA(S)[S]} proved by other authors to show that normal first countable linearly H-closed spaces with various additional properties are compact in these models.

in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

The derivation of a Hardy field induces on its value group a certain function ψ. If a Hardy field extends the real field and is closed under powers, then its value group is also a vector space over R. Such “ordered vector spaces with ψ-function” are called H-couples. We define closed H-couples and show that every H-couple can be embedded into a closed one. The key fact is that closed H-couples ...

In order to overcome disadvantages of traditional single machine mobile video surveillance and intelligence gathering system, such as higher technical complexity, more expensive, and more slowly, a new android-based vehicular distributed intelligent video collection system is integrated by GPS, photograph, camera, network communication, 3G, IPC, H.264 encoder/decoder, wireless communication and...