Convergence and Stability of a Perturbed Mann Iterative Algorithm with Errors for a System of Generalized Variational-Like Inclusion Problems in \(q\)-uniformly smooth Banach Spaces

Authors

  • Jong Kyu Kim Department of Mathematics Education, Kyungnam University, Changwon, Gyeongnam 51767
  • Mohammad Iqbal Bhat Department of Mathematics, South Campus University of Kashmir, Anantnag 192101
  • Sumeera Shafi Department of Mathematics, University of Kashmir, Srinagar 190006

DOI:

https://doi.org/10.26713/cma.v12i1.1401

Keywords:

System of generalized variational-like inclusion problem, \(\mathcal{H}(., .)\)-\(\phi-accretive operator, q-uniformly smooth Banach spaces, resolvent operator technique, perturbed Mann iterative method with errors, convergence analysis, stability analysis

Abstract

In this paper, we introduce a class of \({\cal H}(\cdot,\cdot)\)-\(\phi\)-\(\eta\)-accretive operators in a real \(q\)-uniformly smooth Banach space. We define the resolvent operator associated with \({\cal H}(\cdot,\cdot)\)-\(\phi\)-\(\eta\)-accretive operator and prove that it is single-valued and Lipschitz continuous. Moreover, we propose a perturbed Mann iterative method with errors for approximating the solution of the system of generalized variational-like inclusion problems and discuss the convergence and stability of the iterative sequences generated by the algorithm. Our results presented in this paper generalize and unify many known results in the literature.

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References

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Published

31-03-2021
CITATION

How to Cite

Kim, J. K., Bhat, M. I., & Shafi, S. (2021). Convergence and Stability of a Perturbed Mann Iterative Algorithm with Errors for a System of Generalized Variational-Like Inclusion Problems in \(q\)-uniformly smooth Banach Spaces. Communications in Mathematics and Applications, 12(1), 29–50. https://doi.org/10.26713/cma.v12i1.1401

Issue

Vol. 12 No. 1 (2021)

Section

Research Article

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