Convergence Theorems For Finite Family Research Articles

Strong Convergence Theorem for Finite Family of Asymptotically Nonexpansive in the Intermediate Sense Nonself Maps

Let K be a nonexpansive retract of a uniformly convex Banach space X with retraction P. Let Ti: K → X (i= 1,...,m) be a finite family of uniformly continuous asymptotically nonexpansive in the intermediate sense maps with a nonempty common fixed points set F. Sufficient conditions for the strong convergence of a sequence of successive approximations generated by an m-step algorithm to a point of F are proved.MSC(2010): 47H10, 47J25

Strong Convergence Theorem for Finite Family of Generalised Asymptotically Nonexpansive Maps

Let K be a nonexpansive retract of a uniformly convex Banach space X with retraction P and Ti:1 · · ·,m: K-> X a finite family of uniformly continuous generalised asymptotically nonexpansive maps with a nonempty common fixed point set F. We provided and proved sufficient conditions for the strong convergence of a sequence of successive approximations generated by an m-step algorithm to a point of F.

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

Let H be a real Hilbert space, K a nonempty subset of H, and $T:K\rightarrow \mathit{CB}(K)$ a multi-valued mapping. Then T is called a generalized k-strictly pseudo-contractive multi-valued mapping if there exists $k\in[0,1)$ such that, for all $x,y\in D(T)$ , we have $D^{2}(Tx,Ty)\leq\|x-y\|^{2}+kD^{2}(Ax,Ay)$ , 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.

Convergence Theorems for Finite Family of Multivalued Maps in Uniformly Convex Banach Spaces

We introduce a new iterative process to approximate a common fixed point of a finite family of multivalued maps in a uniformly convex real Banach space and establish strong convergence theorems for the proposed process. Furthermore, strong convergence theorems for finite family of quasi-nonexpansive multivalued maps are obtained. Our results extend important recent results.

Convergence theorem for finite family of lipschitzian demi-contractive semigroups

Let E be a real Banach space and K be a nonempty, closed, and convex subset of E. Let be a finite family of Lipschitzian demi-contractive semigroups of K, with sequences of bounded measurable functions L i : [0, ∞) → (0, ∞) and bounded functions λ i : [0, ∞) → (0, ∞), respectively, where , i = 1,2, ..., N. Strong convergence theorem for common fixed point for finite family is proved in a real Banch space. As an application, a new convergence theorem for finite family of Lipschitzian demi-contractive maps is also proved.Mathematics subject classification (2000) 47H09, 47J25