Approximating fixed points of non-self asymptotically nonexpansive mappings in Banach spaces

Approximating Fixed Points of Non-self Asymptotically Nonexpansive Mappings in Banach Spaces

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be an asymptotically nonexpansive mapping with {kn} ⊂ [1,∞) such that ∑∞ n=1(kn − 1) <∞ and F(T) is nonempty, where F(T) denotes the fixed points set of T . Let {αn}, {α′n}, and {α′′ n } be real sequences in (0,1) and ≤ αn,α′n,α′′ n ≤ 1− for all...

Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections

for all x, y ∈ C and each n ≥ 1. The class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [1] as an important generalization of nonexpansive mappings. It was proved in [1] that if C is a nonempty bounded closed convex subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self mapping on C, then F (T ) is nonempty closed convex subset o...

On fixed points of fundamentally nonexpansive mappings in Banach spaces

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

Approximating fixed points for nonexpansive mappings and generalized mixed equilibrium problems in Banach spaces

We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results...

Approximating fixed points of generalized nonexpansive mappings