Approximation of common fixed points of a countable family of continuous pseudocontractions in a uniformly smooth Banach space

AbstractIn this paper, we introduce a new implicit iterative algorithm for finding a common element of a countable family of continuous pseudocontractions in a uniformly smooth Banach space. We obtain some strong convergence theorems under suitable conditions. Our results extend the recent results announced by many others

Generalized Delta Theorems for Multivalued Mappings and Measurable Selections

The classical delta theorem can be generalized in a mathematically satisfying way to a broad class of multivalued and/or nonsmooth mappings, by examining the convergence in distribution of the sequence of difference quotients from the perspectives of recent developments in convergence theory for random closed sets and new descriptions of first-order behavior of multivalued mappings. Such a theory opens the way to applications of asymptotic techniques in many areas of mathematical optimization where randomness and uncertainty play a role. Of special importance is the asymptotic convergence of measurable selections of multifunctions when the limit multifunction is single-valued almost surely