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<p>We investigate the convergence properties of the SRJ iterative process for a class of nonlinear operators, namely those satisfying condition (E), in the framework of <i>W</i>-hyperbolic spaces. This class contains, as particular cases, nonexpansive mappings and mappings satisfying condition (C), thus extending the scope of existing convergence theory. We establish strong and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varDelta \)</EquationSource> </InlineEquation>-convergence theorems, providing rigorous guarantees for the applicability of the method in this setting. The theoretical results are supported by numerical experiments demonstrating the superior performance of the SRJ method under various parameter choices. Furthermore, we illustrate the practical relevance of the method by applying it to approximate fixed points of a nonlinear Urysohn integral operator in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2([0,1])\)</EquationSource> </InlineEquation>, confirming its computational efficiency in functional analytic applications. These contributions extend and unify a range of existing results, offering an effective tool for fixed point problems in nonlinear analysis.</p>

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On SRJ iteration of E-operators in hyperbolic spaces with numerical analysis and application

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Jaynendra Shrivas,
  • Dan I. Ricinschi

摘要

We investigate the convergence properties of the SRJ iterative process for a class of nonlinear operators, namely those satisfying condition (E), in the framework of W-hyperbolic spaces. This class contains, as particular cases, nonexpansive mappings and mappings satisfying condition (C), thus extending the scope of existing convergence theory. We establish strong and \(\varDelta \) -convergence theorems, providing rigorous guarantees for the applicability of the method in this setting. The theoretical results are supported by numerical experiments demonstrating the superior performance of the SRJ method under various parameter choices. Furthermore, we illustrate the practical relevance of the method by applying it to approximate fixed points of a nonlinear Urysohn integral operator in \(L^2([0,1])\) , confirming its computational efficiency in functional analytic applications. These contributions extend and unify a range of existing results, offering an effective tool for fixed point problems in nonlinear analysis.