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In a real Hilbert space, an iterative scheme is considered to obtain a common fixed point for a countable family of nonexpansive mappings. In addition, strong convergence to the common fixed point of this sequence is investigated. As an application, an equilibrium problem is solved. We also state more applications of this procedure to obtain a common fixed point of W-mappings. [ABSTRACT FROM AUTHOR]

In this paper, new classes of rational Geraghty contractive mappings in the setup of b-metric spaces are introduced. Moreover, the existence of some fixed point for such mappings in ordered b-metric spaces are investigated. Also, some examples are provided to illustrate the results presented herein. Finally, an application of the main result is given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of an α3-proximal admissible mappings and establish the existence of best proximity point theorems for implicit relation type modified α3-proximal contractions. As applications of our theorems, we derive some new best proximity point results for implicit relation type contractions whenever the range space is endowed with a graph or with a partial order. The obtained results generalize, extend, and modify some best proximity point results in the literature. Several interesting consequences of our theorems are also provided. [ABSTRACT FROM AUTHOR]