Strong convergence theorems for strongly monotone mappings in Banach spaces

Mathew O. Aibinu; Oluwatosin Mewomo

doi:10.5269/bspm.37655

Mathew O. Aibinu University of Kwazulu https://orcid.org/0000-0003-4901-1440
Oluwatosin Mewomo University of Kwazulu https://orcid.org/0000-0003-0389-7469

Resumo

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 \cite{b1}, 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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Biografia do Autor

Mathew O. Aibinu, University of Kwazulu

GRADUATE STIDENT, SCHOOL OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE, UNIVERSITY OF KWAZULU-NATAL, DURBAN, SOUTH AFRICA

Oluwatosin Mewomo, University of Kwazulu

SENIOR LECTURER, SCHOOL OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE, UNIVERSITY OF KWAZULU-NATAL, DURBAN, SOUTH AFRICA

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