In this paper, we obtain some fixed point results for noncyclic monotone ρ-nonexpansive mappings in uniformly convex modular spaces and uniformly convex in every direction modular spaces. As an application, we prove the existence of the solution of an integral equation.

In this paper, we introduce and study some properties of a new class of generalized monotone nonexpansive mappings in hyperbolic metric spaces. Further, we give some results on the convergence of the Mann iterative process for this class of mappings in hyperbolic ordered metric spaces with some interesting examples.

In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups.

In this paper, we discuss a class of mappings more general than ρ-nonexpansive mapping defined on a modular space endowed with a graph. In our investigation, we prove the existence of fixed point results of these mappings. Then, we also introduce an iterative scheme for which proves the convergence to a fixed point of such mapping in a modular space with a graph.