This study introduce a new type of closed sets in topology called Generalized h-closed (briefly, gh-closed) define as follow: E ⊆ χ be gh-closed set if CLh (E)⊆ U whenever and is open (χ,τ). The relation between other classes ( h-closed, g-closed, g -closed, g-closed αg-closed) are studied. Also, the notion gh-continuous mapping on topological space some properties proved. Finally, separation a...

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...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...

The aim of the paper is to first investigate some properties of the hyperspace $theta(X)$, and then in the next article it deals with some detailed study of a special type of subspace $downarrowtheta C(X)$ of the space $theta (Xtimes mathbb I)$.

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...

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize thei...

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...

We study chains in an H-closed topological partially ordered space. We give sufficient conditions for a maximal chain L in an H-closed topological partially ordered space such that L contains a maximal (minimal) element. Also we give sufficient conditions for a linearly ordered topological partially ordered space to be H-closed. We prove that any H-closed topological semilattice contains a zero...