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 optimal (Monge-Kantorovich) transportation problem is discussed from several points of view. The Lagrangian formulation extends the action of the Lagrangian L(v, x, t) from the set of orbits in Rn to a set of measure-valued orbits. The Eulerian, dual formulation leads an optimization problem on the set of sub-solutions of the corresponding Hamilton-Jacobi equation. Finally, the Monge proble...

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...

K e y w o r d s G a u s s N e w t o n ' s method, Lipschitz conditions with L average, Convergence ball, Uniqueness bali. 1. I N T R O D U C T I O N Finding the solution of a nonlinear operator equation f(x) = 0 (1.1) in Banach space X is a very general subject which is widely used in both theoretical and applied areas of mathematics, where f is a nonlinear operator from some domain D in a real...