Implicit Iteration Scheme with Perturbed Mapping for Common Fixed Points of a Finite Family of Lipschitz Pseudocontractive Mappings

Let E be a real Banach space, {Ti}i=1 be a finite family of continuous pseudocontractive self mappings of E and G : E → E be a mapping which is both δ -strongly accretive and λ -strictly pseudocontractive of Browder-Petryshyn type such that δ + λ 1 . We propose a new implicit iteration scheme with perturbed mapping G for the approximation of common fixed points of {Ti}i=1 . For an arbitrary initial point x0 ∈ E , the sequence {xn}∞n=1 is defined by xn = αn(xn−1 − λnG(xn−1)) + (1 − αn)Tnxn where Tn = Tn mod N , {αn}∞n=1 ⊂ [a, b] ⊂]0, 1[ and {λn}∞n=1 ⊂ [0, 1[ . We establish some weak convergence theorems for this implicit iteration scheme. Also, necessary and sufficient conditions for strong convergence of this implicit iteration scheme are obtained.