We prove the following completeness theorem: If the fixed point operation over a category is defined by initial@, then the equations satisfied by the fixed point operation are exactly those of iteration theories. Thus, in such categories, the equational axioms of iteration theories provide a sound and complete axiomatization of the equational properties of the fixed point operation.

In this paper, we propose a three-step iteration scheme for nonself asymptotically nonexpansive type mappings in a complete CAT(0) metric space and establish necessary and sufficient conditions for convergence of this process to a fixed point of nonself asymptotically nonexpansive type mappings. We also establish a strong convergence result. These results generalize and unify many important res...

We show that every automorphism α of a free group Fk of finite rank k has asymptotically periodic dynamics on Fk and its boundary ∂Fk: there exists a positive power α such that every element of the compactum Fk ∪ ∂Fk converges to a fixed point under iteration of α . Further results about the dynamics of α as well as an extension from Fk to word-hyperbolic groups are given in the later sections.

In this paper, we consider a new random iteration process to approximate a common random fixed point of a finite family of uniformly quasi-Lipschitzian random mappings in generalized convex metric spaces. Our results presented in this paper extend and improve several recent results. c ©2016 All rights reserved.

The purpose of this paper is to study the convergence of a new finite steps iterative sequence with mean errors to a common fixed point for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend and generalize some results in the literature.

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the proposed iterative scheme under some appropriate conditions.

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. Keywords—Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

We present a practical algorithm for computing exact least solutions of systems of equations over the rationals with addition, multiplication with positive constants, minimum and maximum. The algorithm is based on strategy improvement combined with solving linear programming problems for each selected strategy. We apply our technique to compute the abstract least fixpoint semantics of affine pr...

The purpose of this paper is to study the weak and strong convergence of an new implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve important known results in [1], [2], [4]–[9], [11]–[15] and others.