Subgradients of Distance Functions at Out-of-Set Points

Fuzzy Best Simultaneous Approximation of a Finite Numbers of Functions

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

On the Subdifferentiability of Convex Functions

(Thus the subgradients of / correspond to the nonvertical supporting hyperplanes to the convex set consisting of all the points of E®R lying above the graph of /.) The set of subgradients of / at x is denoted by dfix). If d/(x) is not empty, / is said to be subdifferentiable at x. If/actually had a gradient x* = V/(x) at x in the sense of Gateaux (or Frechet), one would in particular have d/(x)...

Common fixed points for a pair of mappings in $b$-Metric spaces via digraphs and altering distance functions

In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying some generalized contractive type conditions in $b$-metric spaces endowed with graphs and altering distance functions. Finally, some examples are provided to justify the validity of our results.

Completeness in Probabilistic Metric Spaces

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...