Existence and Approximation of Best Proximity Points and Fixed Points of Cyclic Generalized \(\vartheta \)-Contraction Maps

In this paper, we introduce a new class of maps, called cyclic generalized \(\vartheta \) $\vartheta$ -contractions, which contains the generalized \(\varphi \) $\phi$ -contractions as a subclass. Using the concept of WUC property on a metric space, we prove convergence and existence results of the best proximity points for this class of contractions. These results extend and improve best proximity point results of the generalized \(\varphi \) $\phi$ -contractions. Also, we find a priori and a posteriori error estimates of the fixed point for the Picard iteration associated with a cyclic generalized \(\vartheta \) $\vartheta$ -contraction map, which is defined on a complete metric space