Coincidence and common fixed point theorems for b-quasi contractive mappings on metric spaces endowed with binary relations and involving suitable comparison functions are presented. Our results generalize, improve, and extend several recent results. As an application, we study the existence of solutions for some class of integral equations.
In this paper, we search some best proximity point results for a new class of non-self mappings T : A − → B called α-proximal Geraghty mappings. Our results extend many recent results appearing in the literature. We suggest an example to support our result. Several consequences are derived. As applications, we investigate the existence of best proximity points for a metric space endowed with symmetric binary relation.
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