Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces

A Projection Method for Relatively Nonexpansive Mappings in Banach Spaces

We introduce a new projection algorithm for solving the fixed point problem of relatively nonexpansive mappings in the framework of Banach spaces. We also prove the strong convergence theorem for such mappings. Mathematics Subject Classification: 47H09, 47H10

New hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces

In this paper, applying hybrid projection method, a new modified Ishikawa iteration scheme is presented for finding a common element of the solution set of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in Banach spaces. A numerical example is given and the numerical behaviour of the sequences generated by this algorithm is compared with several existence...

On the Weak Relatively Nonexpansive Mappings in Banach Spaces

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...

Generalized α-nonexpansive mappings in Banach spaces

We consider a new type of monotone nonexpansive mappings in an ordered Banach space X with partial order . This new class of nonlinear mappings properly contains nonexpansive, firmly-nonexpansive and Suzuki-type generalized nonexpansive mappings and partially extends α-nonexpansive mappings. We obtain some existence theorems and weak and strong convergence theorems for the Mann iteration. Some ...