Abstract
This article aims to define a new resolvent operator for variational inclusion problems in the framework of Banach spaces. We design a rapid algorithm using the resolvent operator to approximate the solution of the variational inclusion problem in Banach spaces. Additionally, we show that the algorithm articulated in this article converges faster than the well-known and notable algorithm due to Fang and Huang. To show the superiority and prevalence of the obtained results, we propound a numerical and computational example upholding our claim. Lastly, a minimization problem is solved with the help of the proposed algorithm, which is the first attempt in the current context of the study.
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