Convergence theorems and base properties on condition (C)
Ali Asghar Gholipoor · Pure Mathematical Sciences · 2013
Copyright c © 2013 Ali Asghar Gholipoor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A mapping T on subset C of Banach space E is called no expansive and quasi-no expansive, if for each x, y, z ∈ F (T), we have ‖y − x ‖ ≤ ‖Ty − Tx‖, ‖z − x ‖ ≥ ‖z − Tx‖, where F (T) is the set of fixed points of mapping T. That in this research we introduce some conditions on mappings that are weaker than no expansive condition and stronger than qusi-no expansive condition and by fixed points theorems and con-vergence theorems, we prove fixed point for these set of mappings.