We present new semilocal convergence theorems for Newton methods in a Banach space. Using earlier general conditions we find more precise error estimates on the distances involved using the majorant principle. Moreover we provide a better information on the location of the solution. In the special case of Newton’s method under Lipschitz conditions we show that the famous Newton–Kantorovich hypo...

Hongmin Ren College of Information and Engineering, Hangzhou Polytechnic, Hangzhou 311402, Zhejiang, PR China Email:[email protected] Abstract.We present new sufficient semilocal convergence conditions for the Newton-Kantorovich method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Examples are given to show that our results apply but earlier on...

The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton’s method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for these equations. Finally, we illustrate the above with two particular Fredholm integral equations.

In the present paper we prove a Besicovich weighted ergodic theorem for positive contractions acting on Orlich-Kantorovich space. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices. Mathematics Subject Classification: 37A30, 47A35, 46B42, 46E30, 46G10.

In this paper, introducing a general modification of the classical SzászMirakjan-Kantorovich (SMK) operators, we study their global approximation behavior. Some special cases are also presented.

We present a (semilocal) Kantorovich{type analysis for Newton{like methods for singular operator equations using outer inverses. We establish sharp generalizations of the Kantorovich theory and the Mysovskii theory for operator equations when the derivative is not necessarily invertible. The results reduce in the case of an invertible derivative to well{known theorems of Kantorovich and Mysovsk...

The Monge-Kantorovich mass transport problem is to find the transport plan that minimizes the cost (1). This was formulated by Kantorovich in the 1940's, generalizing Monge's format in 1781. Monge's original formulation of the problem assumes that and asks for BßC œ lBCl a b the existence of a mass-preserving map from the support, Spt ,of 0 a b . . to Spt that minimizes a b / the cost ( a b a ...

These operators were generalized by Dog̃ru in [6]. A Stancu type generalization of these operators has been studied by Agratini [1] and Kantorovich type generalization of Agratini’s operators were constructed and statistical approximation properties were examined by Dog̃ru, Duman and Orhan in [8]. A Kantorovich type generalization of MKZ operators can also be found in [7]. In 2000, Trif [18] intr...

We solve optimal transportation problem using stochastic optimal control theory. Indeed, for a super linear cost at most quadratic at infinity, we prove Kantorovich duality theorem by a zero noise limit (or vanishing viscosity) argument.. We also obtain a characterization of the support of an optimal measure in Monge-Kantorovich minimization problem (MKP) as a graph. Our key tool is a duality r...