We introduce a new iterative method for approximating a locally unique solution of variational inclusions in Banach spaces by using generalized divided differences of the first order. This method extends a method considered by Traub [17] (in the scalar case) and by Potra [12] (in the Banach spaces case) for solving nonlinear equations to variational inclusions. An existence–convergence theorem ...

We introduce and study a new system of random nonlinear generalized variational inclusions involving random fuzzy mappings and set-valued mappings with H ·, · -monotonicity in two Hilbert spaces and develop a new algorithm which produces four random iterative sequences. We also discuss the existence of the random solutions to this new kind of system of variational inclusions and the convergence...

Necessary and sufficient conditions are given so that the space C(X, E) of all continuous functions from a zero-dimensional topological space X to a nonArchimedean locally convex space E, equipped with the topology of uniform convergence on the compact subsets of X, to be polarly absolutely quasi-barrelled, polarly אo-barrelled, polarly `∞-barrelled or polarly co-barrelled. Also, tensor product...

We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse stronglymonotonemappings, the set of solutions of an equilibrium problem, and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated...

We analyze the regularized least square algorithm in learning theory with Reproducing Kernel Hilbert Spaces (RKHS). Explicit convergence rates for the regression and binary classification problems are obtained in particular for the polynomial and Gaussian kernels on the n-dimensional sphere and the hypercube. There are two major ingredients in our approach: (i) a law of large numbers for Hilber...

Abstract: In this paper, we introduce and study the extended Newton-type method for solving the variational inclusion 0∈ f (x)+g(x)+F(x), where f :Ω⊆X→Y is Fréchet differentiable in a neighborhood Ω of a point x̄ in X, g:Ω⊆X→Y is linear and differentiable at point x̄, and F is a set-valued mapping with closed graph acting in Banach spaces X and Y. Semilocal and local convergence of the extended N...

Abstract A “Bochner-type” integral for vector lattice-valued functions with respect to (possibly infinite) measures is presented abstract convergences, satisfying suitable axioms, and some fundamental properties are studied. Moreover, by means of this integral, convergence results on operators in modulars proved. Some applications given moment kernels the Brownian motion.