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arXiv · 2008.07888

Strong convergence theorems for strongly monotone mappings in Banach spaces

Mathew O. Aibinu·O. T. Mewomo
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Abstract

Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone and satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired by Alber [2], we introduce Lyapunov functions and use the new geometric properties of Banach spaces to show the strong convergence of an iterative algorithm to the solution of $Ax=0$.

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BibTeXRIS

Mathew O. Aibinu, O. T. Mewomo. 2020-08-18. Strong convergence theorems for strongly monotone mappings in Banach spaces. https://doi.org/10.5269/bspm.37655

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