相关论文: Frechet and Mordukhovich Derivative (Coderivative)…
In this paper, we calculate the covering constants for single-valued mappings in Euclidean space by using Mordukhovich derivatives (or coderivatives). At first, we prove the guideline for calculating the Frechet derivatives of single-valued…
We continue the study in part I for calculating the Frechet derivatives and Mordukhovich derivatives (coderivatives) and covering constants for single-valued mappings in Euclidean spaces (It is part I). In this paper, we particularly…
In this paper, we use the Mordukhovich derivatives to precisely find the covering constants for the metric projection operator onto nonempty closed and convex subsets in uniformly convex and uniformly smooth Banach spaces. We consider three…
In this paper, we investigate some properties of the Mordukhovich derivatives of the normalized duality mapping in Banach spaces. For the underlying spaces, we consider three cases: uniformly convex and uniformly smooth Banach space lp;…
Mordukhovich derivatives (Mordukhovich coderivatives) of set-valued mappings in Banach spaces have firmly laid the foundation of the theory of generalized differentiation in set-valued analysis, which has been widely applied to optimization…
In this paper, we investigate the properties and the precise solutions of the Mordukhovich derivatives of the set-valued metric projection operator onto some closed balls in some general Banach spaces. In the Banach space c, we find the…
In this paper, we will define generalized critical point, ordered extreme and order monotone property of single-valued mappings in partially ordered Banach spaces. In particular, we will find the explicit formulas of Gateaux and Frechet…
In this paper, we investigate the properties of the Mordukhovich derivatives of the metric projection operator onto closed balls, closed and convex cylinders and positive cones in uniformly convex and uniformly smooth Banach spaces. We find…
We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad-Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of…
In this paper, we investigate some fixed-point properties of the Mordukhovich differential operator of set valued mappings (or, single valued mappings) on Banach spaces. In particular, we study the fixed-point properties of the Mordukhovich…
In this paper we give some results concerning Frechet differentiable mappings between domains in normed spaces with controlled growth. The results are mainly motivated by Pavlovic's equality for the Bloch semi-norm of continuously…
Differentiation in mathematical analysis is commonly built by using {\epsilon}-{\delta}-language. This approach also works similarly for defining continuity, Gateaux (directional) derivative and Frechet derivative in normed vector spaces,…
In this paper, the concept of coderivatives at infinity of set-valued mappings is introduced. Well-posedness properties at infinity of set-valued mappings as well as Mordukhovich's criterion at infinity are established. Fermat's rule at…
We consider the problem of estimating the Fr\'echet and conditional Fr\'echet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator…
For a set-valued map, we characterize, in terms of its (unconvexified or convexified) graphical derivatives near the point of interest, positively homogeneous maps that are generalized derivatives in the sense of [20]. This result…
The Chebyshev points are commonly used for spectral differentiation in non-periodic domains. The rounding error in the Chebyshev approximation to the $n$-the derivative increases at a rate greater than $n^{2m}$ for the $m$-th derivative.…
This paper introduces a new approach for the computation of electromagnetic field derivatives, up to any order, with respect to the material and geometric parameters of a given geometry, in a single Finite-Difference Time-Domain (FDTD)…
The purpose of this paper is to show and explain a new formula that indicates with finality the derivatives of Shifted Monic Ultraspherical polynomials (SMUPs) of any degree and for any fractional-order using the shifted Monic…
In Part 1 of this paper, we have estimated the Fr\'echet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total…
In this work derivations of definite integrals listed in Prudnikov volume I, Gradshteyn and Ryzhik and a few other tables are produced. Special cases of these integrals in terms of fundamental constants are also evaluated. The method used…