Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X, ‖ · ‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = R this construction yields a norm such that D(R) becomes a Banach space. Furthermore, we show that for a real Banach space...

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.

We consider complementarity problems involving functions which are not Lipschitz continuous at the origin. Such problems arise from the numerical solution for differential equations with non-Lipschitzian continuity, e.g. reaction and diffusion problems. We propose a regularized projection method to find an approximate solution with an estimation of the error for the nonLipschitzian complementar...

Two fixed point theorems for uniformly lipschitzian mappings in metric spaces, due respectively to E. Lif̌sic and to T.-C. Lim and H.-K. Xu, are compared within the framework of the so-called CAT(0) spaces. It is shown that both results apply in this setting, and that Lif̌sic’s theorem gives a sharper result. Also, a new property is introduced that yields a fixed point theorem for uniformly lipsc...

We obtain local estimates of the distance to a set defined by equality constraints under assumptions which are weaker than those previously used in the literature. Specifically, we assume that the constraints mapping has a Lipschitzian derivative, and satisfies a certain 2-regularity condition at the point under consideration. This setting directly subsumes the classical regular case and the tw...

Let X be a real Banach space. A multivalued operator T from K into 2 is said to be pseudo-contractive if for every x, y in K, u ∈ T (x), v ∈ T (y) and all r > 0, ‖x−y‖ ≤ ‖(1+r)(x−y)−r(u−v)‖. Denote by G(z, w) the set {u ∈ K : ‖u−w‖ ≤ ‖u−z‖}. Suppose every bounded closed and convex subset of X has the fixed point property with respect to nonexpansive selfmappings. Now if T is a Lipschitzian and ...

Let E be a real Banach space with uniformly Gâteaux differentiable norm possessing uniform normal structure. K is a nonempty bounded closed convex subset of E, and { } ( ) ... , 2 , 1 = n Tn is a sequence of − n k Lipschitzian nonexpansive mappings from K into itself such that 1 lim = ∞ → n n k and ( ) 0 1 / ≠ ∞ = n n T F ∩ and f be a contraction on K. Under sutiable conditions on sequence { },...

In this article, we consider an unconstrained minimization formulation of the nonlinear complementarity problem NCP(f) when the underlying functions are H-differentiable but not necessarily locally Lipschitzian or directionally differentiable. We show how, under appropriate regularity conditions on an H-differential of f , minimizing the merit function corresponding to f leads to a solution of ...

This paper is a contribution to the sensitivity analysis of piecewise smooth equations. A piecewise smooth function is a Lipschitzian homeomorphism near a given point if and only if it is coherently oriented and has an invertible B-derivative at this point. We emphasise the role of functions of the type f = g h where g is piecewise smooth and h is smooth and present veriiable conditions which e...