‎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( ...

The generalization of binary operation in the classical algebra to fuzzy is an important development field algebra. paper proposes a new vector spaces over field, which called M-hazy field. Some fundamental properties spaces, and subspaces are studied, some results also proved. Furthermore, linear transformation studied their Finally, it shown that M-fuzzifying convex induced by subspace space.

Within the categoryW of archimedean lattice-ordered groups with weak order unit, we show that the objects of the form C (L), the set of continuous real-valued functions on a locale L, are precisely those which are divisible and complete with respect to a variant of uniform convergence, here termed indicated uniform convergence. We construct the corresponding completion of aW-object A purely alg...

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...