A General Picard-Mann Iterative Method for Approximating Fixed Points of Nonexpansive Mappings with Applications

Fixed point theory provides an important structure for the study of symmetry in mathematics. In this article, a new iterative method (general Picard–Mann) to approximate fixed points of nonexpansive mappings is introduced and studied. We study the stability of this newly established method which we find to be summably almost stable for contractive mappings. A number of weak and strong convergence theorems of such iterative methods are established in the setting of Banach spaces under certain geometrical assumptions. Finally, we present a number of applications to address various important problems (zero of an accretive operator, mixed equilibrium problem, convex optimization problem, split feasibility problem, periodic solution of a nonlinear evolution equation) appearing in the field of nonlinear analysis.