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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 4
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An algorithm for computing zeros of generalized phi-strongly monotone and bounded maps in classical Banach spaces

C.E. ChidumeDepartment of Pure and Applied Mathematics, African University of Science and Technology, Abuja, Nigeria.Correspondence[email protected]
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C.O. ChidumeDepartment of Mathematics, Auburn University, Auburn, USA.View further author information
&
A.U. BelloDepartment of Pure and Applied Mathematics, African University of Science and Technology, Abuja, Nigeria.;Department of Mathematical Science and Information Technology, Federal University, Dutsin-Ma, Nigeria.View further author information
Pages 827-839 | Received 16 Mar 2015, Accepted 10 Jul 2015, Published online: 14 Aug 2015
 
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Abstract

Let , , and be a generalized -strongly monotone and bounded map with . An iterative process is constructed and proved to converge strongly to the unique solution of the equation . In the special case in which is the subdifferential of a proper convex function , a solution of corresponds to a minimizer of . Furthermore, our technique of proof is of independent interest.

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Notes

No potential conflict of interest was reported by the authors.

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Funding

This research was supported by ACBF Research Grant Funds to AUST.

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