Fixed points for iterates

Normal Families and Fixed Points of Iterates

Let F be a family of holomorphic functions and suppose that there exists ε > 0 such that if f ∈ F , then |(f2)′(ξ)| ≤ 4 − ε for all fixed points ξ of the second iterate f. We show that then F is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p has a fixed point ξ such that |(p2)′(ξ)| ≥ 4. The results are motivated by a problem posed by Yang...

Fixed Points Results via Iterates of Four Maps in TVS-valued Cone Metric Spaces

: We obtain common fixed points of four mappings satisfying a contractive type condition by demonstrating the convergence of their sequence of iterates in TVS valued cone metric spaces. Our results generalize some well-known recent results in the literature.

Approximate KKT Points for Iterates of an Optimizer

In this technical note, we suggest a new definition for an approximate KKT point. The concept of approximate KKT point can then be used on iterates (points found by an optimization algorithm) to check whether the iterates lead to a KKT point. We will concentrate on the following simple optimization problem (P): Min f(x) subject to gi(x) ≤ 0, i = 1, 2, . . . ,m. (1) We will assume that f and eac...

New iteration process for approximating fixed points in Banach spaces

‎The object of this paper is to present a new iteration process‎. ‎We will show that our process is faster than the known recent iterative schemes‎. ‎We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings‎. ‎We also present a numerical example for proving the rate of convergence of our res...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points