‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...

It is shown that the Vitali convergence theorem remains valid for the -upper integral. Using this result we prove completeness of the space L( ) with respect to the k kp-upper norm for 1 p < 1 , describe convergence of its elements in terms of the space L( ) for 1 p < 1 , give a necessary and sufficient condition for a sequence from L( ) to converge in the k kp-upper norm to a function from L( ...

We prove that the convergence of a sequence of functions in the space L0 of measurable functions, with respect to the topology of convergence in measure, implies the convergence μ-almost everywhere (μ denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space L∞, and also on Orlicz spaces LN with respect to a finitely additive extende...

We study tangential convergence of convolutions with approximate identities of functions defined on a homogeneous type space and having a certain regularity. Our results contain those already known for the Euclidean case and give new ones for stratified nilpotent Lie groups and for solutions of the Dirichlet problem on Lipschitz domains.

the aim of this paper is to introduce and study a new concept of strong double δ ( a ) σ -convergence sequences with respect to an orlicz function, and some properties of the resulting sequencespaces were also examined. in addition, we define the δ ( a ) σ -statistical convergence and establish someconnections between the spaces of strong double δ ( a ) σ -convergence sequences and the space of...

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L−ordered fuzzifying convergence spaces, in which the category of L−fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called th...

the concept of ${mathscr{f}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{f}}$. its equivalence to the concept of ${mathscr{f}}$-convergence in uniform spaces is proved. this convergence generalizes many kinds of convergence, including the well-known statistical convergence.

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...