The classical trust region algorithm was extended to the nonsmooth minimization problem successful by Qi and Sun. Combining the trust region algorithm of Qi and Sun and the trust region algorithm with radius bounded below of Jiang for solving generalized complementarity problems, this paper present a new trust region algorithm with radius bounded below for the unconstrained nonsmooth optimizati...

Certain topological dynamical systems are considered that arise from actions of σ-compact locally compact Abelian groups on compact spaces of translation bounded measures. Such a measure dynamical system is shown to have pure point dynamical spectrum if and only if its diffraction spectrum is pure point.

This paper discusses two common techniques in functional analysis: the topological method and the bornological method. In terms of Pietsch’s operator ideals, we establish the equivalence of the notions of operators, topologies and bornologies. The approaches in the study of locally convex spaces of Grothendieck (via Banach space operators), Randtke (via continuous seminorms) and Hogbe-Nlend (vi...

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B(E) be the Banach algebra of all bounded linear operators on a Banach space E. LetHVb (G,E) andHV0 (G,E) be the weighted locally convex spaces of vector-valued analytic functions. In this survey, we present a development of the theory of multiplication operators and composition operators from classical ...

The purpose of this paper is to study singular integrals whose kernels k(x; ξ) are variable, i.e. they depend on some parameter x ∈ R and in ξ ∈ R \ {0} satisfy mixed homogeneity condition of the form k(x;μξ1, . . . , μ ξn) = μ − ∑ n i=1 ik(x; ξ) with positive real numbers αi ≥ 1 and μ > 0. The continuity of these operators in L(R) is well studied by Fabes and Rivière. Our goal is to extend the...

‎‎The purpose of this paper is to introduce new methods for constructing generalized groups, generalized topological groups and top spaces. We study some properties of these structures and present some relative concrete examples. Moreover, we obtain generalized groups by using of Hilbert spaces and tangent spaces of Lie groups, separately.

We show some estimates and approximation results of operators convolution type de?ned on Riesz Bounded variation spaces in Rn. also state embedding that involve the collection generalized absolutely continuous functions.

— The notion of i-bounded geometry generalises simultaneously bounded geometry and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by constructing a natural Cannon-Thurston map.

In this paper, we define a soft generalized ?-closed set, which is generalization of both the set and closed set. We show that classes sets coincide in anti-locally countable topological spaces. Additionally, locally spaces, every Furthermore, prove space (X,??,A). addition to these, determine behavior relative unions, intersections, subspaces, generated topologies. investigate images inverse u...