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

Jong Kyu Kim, Mohammad Iqbal Bhat, Sumeera Shafi

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.


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

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v12i1.1401

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