Demonstratio Mathematica (May 2024)

A novel iterative process for numerical reckoning of fixed points via generalized nonlinear mappings with qualitative study

  • Ahmad Fayyaz,
  • Ullah Kifayat,
  • Ahmad Junaid,
  • Hammad Hasanen A.,
  • George Reny

DOI
https://doi.org/10.1515/dema-2023-0151
Journal volume & issue
Vol. 57, no. 1
pp. 133 – 181

Abstract

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This manuscript is devoted to constructing a novel iterative scheme and reckoning of fixed points for generalized contraction mappings in hyperbolic spaces. Also, we establish Δ\Delta and strong convergence results by the considered iteration under the class of mappings satisfying condition (E). Moreover, some qualitative results of the suggested iteration, like weak w2{w}^{2}-stability and data dependence results, are discussed. Furthermore, to test the efficiency and effectiveness of the proposed iteration, practical experiments are given. To support the theoretical results, illustrative examples are presented. Finally, our results improve and generalize several classical results in the literature of fixed point iterations.

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