Fixed point iterative methods for generalized monotone nonexpansive mappings

In this project, we intend to: (1) obtain some fixed point results for generalized monotone nonexpansive mappings, namely, monotone mappings satisfying Condition (C), monotone nonexpansive mappings, monotone fundamentally nonexpansive mappings in CAT(0) spaces, hyperbolic spaces and convex metric spaces endowed with a partial order or an oriented graph; (2) investigate some properties of the fixed point sets of generalized monotone nonexpansive mappings; (3) study different iterative methods to approximate fixed points of generalized monotone nonexpansive mappings in CAT(0) spaces, hyperbolic spaces and convex metric spaces endowed with a partial order or an oriented graph; (4) identify, if possible, the fastest iterative method among the methods studied in (3) and also prove which iterative method is stable; (5) find some applications of some of the results obtained in (1)-(3). Our project explores several important aspects of metric fixed point theory of generalized monotone nonexpansive mappings.