In this paper, we study an iteration process introduced by Thakur et al. for Suzuki mappings in Banach spaces, in the new context of modular vector spaces. We establish existence results for a more recent version of Suzuki generalized non-expansive mappings. The stability and data dependence of the scheme for ρ -contractions is studied as well.
We introduce a new class of non-self mappings by means of a condition which is called the (EP)-condition. This class includes proximal generalized nonexpansive mappings. It is shown that the existence of best proximity points for (EP)-mappings is equivalent to the existence of an approximate best proximity point sequence generated by a three-step iterative process. We also construct a CQ-type algorithm which generates a strongly convergent sequence to the best proximity point for a given (EP)-mapping.
A recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure Sn. Issues related to data dependence and the stability of this iterative process are also being studied. Our study is performed in the framework of Banach spaces, in which the symmetry of the associated metric is a fundamental axiom and plays a key role while proving many results of this paper.
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