Derivative of Upper Lipschitzian

Various Lipschitz-like Properties for Functions and Sets I: Directional Derivative and Tangential Characterizations

In this work we introduce for extended real valued functions, defined on a Banach space X, the concept of K directionally Lipschitzian behavior, where K is a bounded subset of X. For different types of sets K (e.g., zero, singleton, or compact), the K directionally Lipschitzian behavior recovers well-known concepts in variational analysis (locally Lipschitzian, directionally Lipschitzian, or co...

Analysis of Direct Searches for Non-Lipschitzian Functions

It is known that the Clarke generalized directional derivative is nonnegative along the limit directions generated by directional directsearch methods at a limit point of certain subsequences of unsuccessful iterates, if the function being minimized is Lipschitz continuous near the limit point. In this paper we generalize this result for non-Lipschitzian functions using Rockafellar generalized ...

Order - Lipschitzian properties of multifunctions with applications to stability of efficient points

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.

Strong convergence results for fixed points of nearly weak uniformly L-Lipschitzian mappings of I-Dominated mappings

In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...

Convergence Theorems For Two Finite Families of Uniformly L-Lipschitzian Mappings