Approximating Fixed Points of Generalized Cyclic Enriched Contraction Mapping Using Ishi Iteration Scheme with Application
DOI:
https://doi.org/10.64229/e7pt2x51Keywords:
Best proximity point, Bianchini contraction, Fixed point, Generalized cyclic enriched contraction, Ishi algorithmAbstract
This study shows the presence and uniqueness of the optimal proximity point for several classes of generalized cyclic enriched contractions, and offers such fundamental results. We provide convergence results for this contraction. We also provide the conditions in which an iterative method can yield the optimal proximity point. To further illustrate the effectiveness of the ishi technique for generalized cyclic enriched contractions, we present a numerical solutions with comparison table and grapshical analysis, which show that our proposed iterative scheme converges faster than the other schemes. Our results are generalization of many comparable results in literature. In addition, the theoretical framework developed in this study extends classical fixed point and best proximity point results by relaxing standard contraction assumptions. The proposed approach allows a broader class of mappings to be analyzed within a unified setting. The convergence analysis is supported by rigorous proofs, ensuring the reliability of the proposed iterative method. Moreover, the numerical experiments validate the theoretical findings and demonstrate the stability and efficiency of the method under different initial conditions. The comparison with existing iterative schemes highlights the superiority of the proposed algorithm in terms of convergence speed and accuracy. These results indicate that the ishi technique is a powerful and flexible tool for solving proximity point problems arising in nonlinear analysis. Consequently, the findings of this study contribute meaningfully to the existing literature and open new directions for further research in generalized contraction mappings and iterative approximation methods.
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