Convergence theorems for finite family of a general class of multi-valued strictly pseudo-contractive mappings

Abstract

Let H be a real Hilbert space, K a nonempty subset of H, and T :, where A := I -T, and I is the identity operator on K. A Krasnoselskii-type algorithm is constructed and proved to be an approximate fixed point sequence for a common fixed point of a finite family of this class of maps. Furthermore, assuming existence, strong convergence to a common fixed point of the family is proved under appropriate additional assumptions. MSC: 47H04; 47H09; 47H10

New Iteration Scheme for Approximating a Common Fixed Point of a Finite Family of Mappings

“…Several algorithms have been introduced by different authors for the approximation of common fixed points of finite family of mappings S i N i�1 , where N ∈ N (the set of nonnegative integers) (see, for example, [12][13][14][15][16][17][18] and references therein). One of the motivations for this aspect of research is the well-known convex feasibility problem which is reducible to the problem of finding a point in the intersection of the set of fixed points of a family of nonexpansive mappings (see, for example, [19,20]).…”

“…where ς i n ∞ n�1 ⊆ (0, 1) for each i and N i�0 ς i n � 1 for each n (see, for example, [13] and references therein).…”