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Browsing by Author "Thakur, Surendra C."

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    Algorithm for solutions of nonlinear equations of strongly monotone type and applications to convex minimization and variational inequality problems
    (Hindawi Limited, 2020-08-01) Aibinu, Mathew O.; Thakur, Surendra C.; Moyo, Sibusiso
    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, {\eta})-strongly monotone type, where {\eta} > 0, p > 1. An example is presented for the nonlinear equations of (p, {\eta})-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.
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    The implicit midpoint procedures for asymptotically nonexpansive mappings
    (Hindawi Limited, 2020-06-06) Aibinu, M. O.; Thakur, Surendra C.; Moyo, S.
    The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper studies the convergence analysis of the class of asymptotically nonexpansive mappings by the implicit midpoint iterative procedures. The necessary conditions for the convergence of the class of asymptotically nonexpansive mappings are established, by using a well-known iterative algorithm which plays important roles in the computation of fixed points of nonlinear mappings. A numerical example is presented to illustrate the convergence result. Under relaxed conditions on the parameters, some algorithms and strong convergence results were derived to obtain some results in the literature as corollaries.