The Krasnosel’skiı̆–Mann (KM) iteration is a widely used method to solve fixed point problems. This paper investigates the convergence rate for the KM iteration. We first establish a new convergence rate for the KM iteration which improves the known big-O rate to little-o without any other restrictions. The proof relies on the connection between the KM iteration and a useful technique on the con...

Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only be studied using their orbits. Therefore the standard notion of chaos is not immediately applicable. However, when a suitable definition is used, it is foun...

Let X be a Banach space and K a nonempty subset of X. The set K is called proximinal if for each x ∈ X, there exists an element y ∈ K such that ‖x − y‖ d x,K , where d x,K inf{‖x − z‖ : z ∈ K}. Let CB K , C K , P K , F T denote the family of nonempty closed bounded subsets, nonempty compact subsets, nonempty proximinal bounded subsets of K, and the set of fixed points, respectively. A multivalu...

In this paper, we consider the convergence of three-step fixed point iterative processes for multivalued nonexpansive mapping with errors, under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the multivalued nonexpansive mapping. Our results extend and improve some recent results.

In this paper, we consider the convergence of three-step fixed point iterative processes for multivalued nonexpansive mapping, under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the multivalued nonexpansive mapping. Our results extend and improve some recent results. Mathematics Subject Classification: 47H09, 47H10, ...

Let E be an arbitrary real Banach space andK a nonempty, closed, convex (not necessarily bounded) subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant L ≥ 1, then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges ...

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated methods been introduced. The main aim this paper is to use coordinate affine structure create an algorithm with technique countable family in Hilbert space symmetric directed graph G and prove the weak theor...

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

We present a modified version of the infeasible-interior- We present a modified version of the infeasible-interior-point algorithm for monotone linear complementary problems introduced by Mansouri et al. (Nonlinear Anal. Real World Appl. 12(2011) 545--561). Each main step of the algorithm consists of a feasibility step and several centering steps. We use a different feasibility step, which tar...