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Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems

Author

Listed:
  • Mathew O. Aibinu
  • Surendra C. Thakur
  • Sibusiso Moyo

Abstract

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.

Suggested Citation

  • Mathew O. Aibinu & Surendra C. Thakur & Sibusiso Moyo, 2020. "Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlaaa:v:2020:y:2020:i:1:n:6579720
    DOI: 10.1155/2020/6579720
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    References listed on IDEAS

    as
    1. C. E. Chidume & N. Djitté, 2012. "Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Yakov Alber & Irina Ryazantseva, 2006. "Nonlinear Ill-posed Problems of Monotone Type," Springer Books, Springer, number 978-1-4020-4396-3, March.
    3. Fumiaki Kohsaka & Wataru Takahashi, 2004. "Strong convergence of an iterative sequence for maximal monotone operators in a Banach space," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-11, January.
    4. Fumiaki Kohsaka & Wataru Takahashi, 2004. "Strong convergence of an iterative sequence for maximal monotone operators in a Banach space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2004(3), pages 239-249.
    5. C. E. Chidume & N. Djitté, 2012. "Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, March.
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