Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.

/pdf/on-projection-algorithms-for-solving-convex-feasibility-2wyotvnuad.pdf

On Projection Algorithms for Solving Convex Feasibility Problems

Iterative algorithms for nonexpansive mappings and maximal monotone operators are investigated. Strong convergence theorems are proved for nonexpansive mappings, including an improvement of a result of Lions. A modification of Rockafellar’s proximal point algorithm is obtained and proved to be always strongly convergent. The ideas of these algorithms are applied to solve a quadratic minimization problem.

Iterative Algorithms for Nonlinear Operators

Viscosity approximation methods for nonexpansive mappings

Strong convergence theorems for resolvents of accretive operators in Banach spaces

Nonlinear operators and nonlinear equations of evolution in Banach spaces

https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-73/issue-6/Fixed-points-of-nonexpanding-maps/bams/1183529119.pdf

Fixed points of nonexpanding maps

THEOREM 1. Under certain regularity conditions, the number of straight lines which are tangent to X at two points s and t of X and such that the unit normals to X at s and t are equal is equal to the number of straight lines which are tangent to X at two points s and t of X and such that the unit normals to X at s and t are unequal, plus the number of selfintersections of X, plus one-half the number of inflection points of X, In Figure 1 the double tangents of the first mentioned kind are drawn solid and the others are dashed.

/pdf/global-theorems-for-closed-plane-curves-4agg505gvt.pdf

Benjamin Halpern

Papers

Fixed points of nonexpanding maps

Global theorems for closed plane curves