We prove a new local upper Lipschitz stability result and the associated local error bound for solutions of parametric Karush–Kuhn–Tucker systems corresponding to variational problems with Lipschitzian base mappings and constraints possessing Lipschitzian derivatives, and without any constraint qualifications. This property is equivalent to the appropriately extended to this nonsmooth setting n...

We show that if the equation mapping is 2-regular at a solution in some nonzero direction in the null space of its Jacobian (in which case this solution is critical; in particular, the local Lipschitzian error bound does not hold), then this direction defines a star-like domain with nonempty interior from which the iterates generated by a certain class of Newtontype methods necessarily converge...

In this paper we examine the basic structure of metric trees and prove fixed point theorems for uniformly Lipschitzian mappings in metric trees.

This paper establishes formulas for approximate subdifferentials of locally Lipschitzian marginal (or optimal value) functions which are not required to attain their infimum.

In this paper, we obtained the convergence of modified Noor iterative scheme for nearly Lipschitzian maps in real Banach spaces. Our results contribute to the literature in this area of re- search.

In this article, we provide a splitting method for solving monotone inclusions in real Hilbert space involving four operators: maximally monotone, monotone-Lipschitzian, cocoercive, and monotone-continuous operator. The proposed takes advantage of the intrinsic properties each operator, generalizing forward–backward–half-forward Tseng’s algorithm with line search. At iteration, our defines step...

Certain fixed point theorems are established for nonlinear semigroups of Lipschitzian mappings defined on nonconvex domains in Hilbert and Banach spaces. Some known results are thus generalized.

We define order-Lipschitzian properties of multifunctions and we investigate local upper order-lipschitzness and ordercalmness of efficient points of a set depending upon a parameter.