Study of variational inequalities, fixed points, and their approximation algorithms constitutes a topic of intensive research efforts, especially within the past 30 years. Many well-known problems arising in various branches of science can be studied by using algorithms which are iterative in their nature. As an example, in computer tomography with limited data, each piece of information implies the existence of a convex set C_i in which the required solution lies.

The problem of finding a point in the intersection is then of crucial interest, and it cannot be usually solved directly. Therefore, an iterative algorithm must be used to approximate such point.

A common method in Hilbert spaces is to use the so-called cyclic sequential scheme, in which every convex set C_i is associated with the metric projection PC_i, from all the Hilbert spaces into C_i. Then, the sequence generated from an initial guess and by cyclically applying each PC_i is studied to ensure the weak convergence to a point in C_∗. In the more general setting of nonexpansive maps, given an initial guess, the existence of the weak limit of the sequence constructed by iterations of a single map is not ensured.

A common way to make certain that such limit exists is to use the Krasnoselskii- Mann method, which consists of substituting the map with a convex combination between the identity and the map itself.

“For the past 30 years or so, the study of the Krasnoselskii-Mann iterative procedures for the approximation of fixed points of nonexpansive mappings and fixed points of some of their generalizations and approximation of zeros of accretive-type operators have been flourishing areas of research.” (Chidume, “Geometric Properties of Banach Spaces and Nonlinear Iterations” - Springer, 2009).

The aim of this special issue is to present the newest and most extended coverage of the fundamental ideas, concepts, and important results related to the topics of interest to this special issue. Potential topics include, but are not limited to:

• Iterative schemes to approximate fixed points of nonexpansive type mappings
• Iterative approximations of zeros of accretive type operators
• Iterative approximations of solutions of variational inequalities problems
• Iterative approximations of solutions of equilibrium problems
• Iterative approximations of common fixed points (and/or common zeros) of families of these mappings

Manuscripts submitted will be considered for publication with the understanding that the same work has not been published and is not under consideration for publication elsewhere.

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/ijmms/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/ according to the following timetable: