A New Approach to the Approximation of Common Fixed Points of an Infinite Family of Relatively Quasinonexpansive Mappings with Applications

and Applied Analysis 3 where 〈·, ·〉 denotes the pairing between E and E∗. Readers are directed to 7 and its review 8 , where the properties of the duality mapping and several related topics are presented. The function φ : E × E → R is defined by φ ( x, y ) ‖x‖ − 2〈x, Jy〉 ∥∥y∥∥2, ∀x, y ∈ E. 1.7 Let T be a mapping from C into E. A point p in C is said to be an asymptotic fixed point 9 of T ifC contains a sequence {xn}which converges weakly to p and limn→∞ xn−Txn 0. The set of asymptotic fixed points of T is denoted by F̂ T . We say that the mapping T is relatively nonexpansive see 10 if the following conditions are satisfied: R1 F T / ∅; R2 φ p, Tx ≤ φ p, x , ∀p ∈ F T ;