Reaching Takahashi-type nonexpansive operators via modular structures with application to best proximity point

In this study, we introduce the concepts of modular Reich-type and modular Chatterjea-type nonexpansive mappings, as natural extensions of their definitions from normed vector spaces to modular vector spaces. After describing the two modular conditions and emphasize their role through some examples, we use them in connection with an iteration procedure for obtaining some fixed point convergence-related conclusions. In addition, a connection between modular Chatterjea-type nonexpansive mappings and Takahashi hybrid operators is analyzed. As a remarkable application, we incorporate modular Reich-type and modular Chatterjea-type nonexpansive mappings together with the iteration process into a modular proximal setting and state some best proximity point results.