In this paper, we introduce and analyze the approximation properties of bivariate generalization for family Kantorovich type exponential sampling series. We derive basic convergence result Voronovskaya theorem proposed Using logarithmic modulus smoothness, establish quantitative estimate order Furthermore, study results generalized Boolean sum (GBS) operator associated with At end, provide a fe...

It is shown that the problem of designing a two-reflector system transforming a plane wave front with given intensity into an output plane front with prescribed output intensity can be formulated and solved as the Monge-Kantorovich mass transfer problem1.

We construct a general type of multivortex solutions of the self-duality equations (the Bogomol'nyi equations) of (2+1) dimensional relativis-tic Chern-Simons model with the non-topological boundary condition near innnity. For such construction we use a modiied version of the Newton iteration method developed by Kantorovich.

In this short note we tie up some loose ends regarding the two-sample matching problem and its connections with the Monge-Kantorovich problem of optimal transportation of mass. By making this connection explicit, we immediately obtain moderate and large deviation principles.

We propose a new algorithm to solve the unbalanced and partial L1-Monge– Kantorovich problems. The proposed method is a first-order primal-dual method that is scalable and parallel. The method’s iterations are conceptually simple, computationally cheap, and easy to parallelize. We provide several numerical examples solved on a CUDA GPU, which demonstrate the method’s practical effectiveness.

This is a continuation of our accompanying paper [18]. We provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established in Beiglböck, Cox and Huesmann [2]. Our proof is based on the adaptation of the Monge-Kantorovich duality in our context, a delicate application of the optional cross-section theorem, and a clever conditioning argument intro...

Halley’s method is a famous iteration method for solving nonlinear equations F (X) = 0. Some Kantorovich-like theorems have been given, including extensions for general spaces. Quasi-Halley methods were proposed too. This paper uses the generalized inverse approach in order to obtain a robust generalized Halley method.