Iterative Approximation of Best Proximity Points of M-T Cyclic Contraction Mappings

In many instances, acquiring a solution for an operator equation by using conventional analytical techniques, even after it has been shown that such a solution exists. One has to know the approximate value of this solution to solve situations like these. In order to do this, the operator equation must first be restructured to take the form of a fixed-point equation (FP). On the FP equation, the most convenient iterative method is used, and the limit of the sequence that is created by this algorithm is, in fact, the value of the FP that is sought for the FP equation, as well as the solutions to the operator equation. The numerical computation of FPs for nonlinear operators is now an interesting research subject in nonlinear analysis owing to its applicability in several fields. Many researchers have developed a wide range of techniques to estimate the FP for various sorts of applications. The primary objective of this paper is to present new iteration schemes for approximating the best proximity point (BPP). The convergence of BPP for M-T cyclic contraction mappings (MTCC-mapping) has been investigated in the context of uniformly convex Banach spaces (UCB-space). The iterations approach proposed by Mann and Ishikawa was taken into account and as a result, some strong convergence results were obtained for the BPP for MTCC-mapping. Furthermore, numerical examples supporting the primary conclusion are provided, and the convergence behavior of the iterations is compared.