A Novel Hybrid Approach to Convergence of Picard-${S_n}$ Iterations for Suzuki Generalized Nonexpansive Mappings
DOI:
https://doi.org/10.29020/nybg.ejpam.v19i2.7506Keywords:
Novel hybrid Picard-${S _{n}}$ iteration; Suzuki generalized nonexpansive maps ; fixed point; convergenceAbstract
Recent investigations indicate that incorporating the Picard iteration into diverse iterative frameworks can significantly enhance convergence properties, as demonstrated in hybrid approaches like Picard-Noor, Picard-S, Picard-Ishikawa, and Picard-Mann. Building upon these insights, we introduce a novel iteration process that integrates the Picard method with the $S_n$ scheme. The effectiveness of this Picard-$S_n$ hybrid is demonstrated through a relevant numerical illustration. In addition, we establish strong as well as weak convergence theorems for Suzuki generalized nonexpansive mappings via this process. As a further application, the proposed approach is utilized to solve delay differential equations.
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Copyright (c) 2026 Muhammad Arif, Kifayat Ullah, Ali Asghar, Muhammad Tariq, Afzal Waqar, Hijaz Ahmad, Jorge E. Macias-Diaz, Angel E. Munoz-Zavala
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