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...

The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich du...

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...

We present a new, simple, and elegant algorithm for computing the optimal mapping for the Monge-Kantorovich problem with quadratic cost. The method arises from a reformulation of the dual problem into an unconstrained minimization of a convex, continuous functional, for which the derivative can be explicitly found. The Monge-Kantorovich problem has applications in many fields; examples from ima...

Uko and Argyros provided in [18] a Kantorovich–type theorem on the existence and uniqueness of the solution of a generalized equation of the form f(u)+g(u) ∋ 0, where f is a Fréchet–differentiable function, and g is a maximal monotone operator defined on a Hilbert space. The sufficient convergence conditions are weaker than the corresponding ones given in the literature for the Kantorovich theo...

We propose a model to describe the optimal distributions of residents and services in a prescribed urban area. The cost functional takes into account the transportation costs (according to a Monge–Kantorovich-type criterion) and two additional terms which penalize concentration of residents and dispersion of services. The tools we use are the Monge–Kantorovich mass transportation theory and the...