LetKbe a nonempty, closed, and convex subset of a real Hilbert spaceH. Suppose thatT:K→2Kis a multivalued strictly pseudocontractive mapping such thatF(T)≠∅. A Krasnoselskii-type iteration sequence{xn}is constructed and shown to be an approximate fixed point sequence ofT; that is,limn→∞d(xn,Txn)=0holds. Convergence theorems are also proved under appropriate additional conditions.

Let q > 1 and let K be a nonempty, closed and convex subset of a q-uniformly smooth real Banach space E. Let T : K → CB(K) be a multi-valued strictly pseudo-contractive map with a nonempty fixed point set. A Krasnoselskii-type iteration sequence {x n } is constructed and proved to be an approximate fixed point sequence of T, i.e., lim n→∞ d(x n , Tx n ) = 0. This result is then applied to prove strong convergence theorems for a fixed point of T under additional appropriate conditions. Our theorems improve several important well-known results. MSC: 47H04; 47H06; 47H15; 47H17; 47J25

In this paper, we introduce a new iterative scheme by a hybrid method and prove a strong convergence theorem of a common element in the set of fixed points of a finite family of closed quasi-Bregman strictly pseudocontractive mappings and common solutions to a system of equilibrium problems in reflexive Banach space. Our results extend important recent results announced by many authors. MSC: 47H09; 47J25