arXiv subjects

Mathew O. Aibinu

Publications and source records attributed to Mathew O. Aibinu.

3 recordsLinked to original sources

arXiv2020

Strong convergence theorems for strongly monotone mappings in Banach spaces

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 $Ax=0$.

math.FA↗

arXiv2020

Algorithm for solutions of nonlinear equations of strongly monotone type and applications to convex minimization and variational inequality problems

Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of (p, η)-strongly monotone type, where η > 0, p > 1. An example is presented for the nonlinear equations of (p, η)-strongly monotone type. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory.

math.FA↗

arXiv2020

Solutions of Nonlinear Operator Equations by Viscosity Iterative Methods

Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of λ-strictly pseudocontractive mappings, solution of α-inverse-strongly monotone mappings, and solution of integral equations of Fredholm type

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