13 papers
Differentiation in Topological Vector Spaces
Jinlu Li
Differentiation in mathematical analysis is commonly built by using ε-δ-language. This approach also works similarly for defining continuity, Gateaux (directional) derivative and F…
Continuity of Metric Projection Operator from C[0, 1] onto Pn with Applications to Mordukhovich Derivatives
Jinlu Li
Let C[0, 1] be the Banach space of all continuous real valued functions on [0, 1]. For an arbitrarily given nonnegative integer n, let Pn denote the set of all polynomials with deg…
Covering Constants for Metric Projection Operator with Applications to Stochastic Fixed-Point Problems
Jinlu Li
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…
Fixed-point properties of the Mordukhovich differential operator
Jinlu Li
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 particu…
Mordukhovich derivatives of the set-valued metric projection operator in general Banach spaces
Jinlu Li
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 g…
Mordukhovich derivatives of the metric projection operator in uniformly convex and uniformly smooth Banach spaces
Jinlu Li
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…
Generalized differentiability of the metric projection operator in Hilbert spaces
Jinlu Li
In this paper, we study the generalized differentiability of the metric projection operator in Hilbert spaces. We find exact expressions for Mordukhovich derivatives for the metric…
Frechet differentiability of the metric projection operator in Banach spaces
Jinlu Li
In this paper, we prove Frechet differentiability of the metric projection operator onto closed balls, closed and convex cylinders and positives cones in uniformly convex and unifo…
Strict Frechet Differentiability of the Metric Projection Operator in Hilbert Spaces
Jinlu Li
In this paper, we prove strict Frechet differentiability of the metric projection operator onto closed balls in Hilbert spaces and onto positive cones in Euclidean spaces. We find…
Directional Differentiability of the Generalized Metric Projection in Banach Spaces
Jinlu Li
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X. In this paper, we consider the generalized metric projection oper…
Directional Differentiability of the Metric Projection in Bochner Spaces
Jinlu Li
In this paper, we consider the directional differentiability of metric projection and its properties in uniformly convex and uniformly smooth Bochner space Lp(S; X), in which (S, A…
Strict Frechet and generalized differentiability of the metric projection operator onto balls in Hilbert spaces
Jinlu Li
In this paper, we prove strict Frechet differentiability of the metric projection operator onto closed balls in Hilbert spaces, and we find exact expressions for Frechet derivative…
Directional Differentiability of the Generalized Metric Projection in Hilbert spaces and Hilbertian Bochner spaces
Jinlu Li, Li Cheng, Lishan Liu +1
Let be a real Hilbert space and a nonempty closed and convex subset of . Let denote the (standard) metric projection operator. In this paper, we st…