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Stability and Convergence Analysis for Set-Valued Extended Generalized Nonlinear Mixed Variational Inequality Problems and Generalized Resolvent Dynamical Systems

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  • Iqbal Ahmad
  • Zahoor Ahmad Rather
  • Rais Ahmad
  • Ching-Feng Wen
  • Efthymios G. Tsionas

Abstract

In this paper, we study a set-valued extended generalized nonlinear mixed variational inequality problem and its generalized resolvent dynamical system. A three-step iterative algorithm is constructed for solving set-valued extended generalized nonlinear variational inequality problem. Convergence and stability analysis are also discussed. We have shown the globally exponential convergence of generalized resolvent dynamical system to a unique solution of set-valued extended generalized nonlinear mixed variational inequality problem. In support of our main result, we provide a numerical example with convergence graphs and computation tables. For illustration, a comparison of our three-step iterative algorithm with Ishikawa-type algorithm and Mann-type algorithm is shown.

Suggested Citation

  • Iqbal Ahmad & Zahoor Ahmad Rather & Rais Ahmad & Ching-Feng Wen & Efthymios G. Tsionas, 2021. "Stability and Convergence Analysis for Set-Valued Extended Generalized Nonlinear Mixed Variational Inequality Problems and Generalized Resolvent Dynamical Systems," Journal of Mathematics, Hindawi, vol. 2021, pages 1-21, July.
    • Handle: RePEc:hin:jjmath:5573833
    DOI: 10.1155/2021/5573833
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