Abstract
In this paper, we propose and analyze a new class of iterative schemes designed to approximate the fixed point of T. The convergent behavior of the scheme is investigated under various geometric assumptions on the space X. Let X be a real Banach space and let CX be a nonempty closed convex subset. Consider a nonexpansive mapping T:CC that is ‖T(x)-T(y)‖≤‖x-y‖ for all x, yC under appropriate conditions on the control parameter. We show that the generated sequence xn defined by
xn+1=1-nxn+nTxn
In this work, we aim to establish a new fixed-point theorem for non-expansive and quasi-nonexpansive mappings in Banach spaces using the D:D. iterative process.
