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Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces

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Abstract

This paper reports the hyperbolic space version of the iterative scheme F. First, under mild conditions, we obtain the Δ and strong convergence of this scheme in the class of mappings enriched with condition (E). To support these results, and to show the high accuracy of the F iterative scheme in the class of mappings enriched with condition (E), we suggest an appropriate numerical example and show that its F iterative scheme is more effective than some other iterative schemes. After this, we establish strong convergence, of this scheme for the general class of contractive-like operators. An example to support this result is also presented and the efficiency of the F iterative scheme is tested with the other iterative schemes. Finally, the weak w2–stability and data dependency results are established. Our findings are new and improve some recent results of the current literature.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, 44000, Pakistan

    Junaid Ahmad & Muhammad Arshad

  2. Department of Mathematics, University of Lakki Marwat, Lakki Marwat, 28420, Khyber Pakhtunkhwa, Pakistan

    Kifayat Ullah

Authors
  1. Junaid Ahmad
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  2. Kifayat Ullah
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  3. Muhammad Arshad
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Correspondence to Junaid Ahmad.

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Dr. Ahmad, Dr. Ullah, and Dr. Arshad contributed equally to this manuscript.

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Ahmad, J., Ullah, K. & Arshad, M. Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces. Numer Algor 91, 1755–1778 (2022). https://doi.org/10.1007/s11075-022-01321-y

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  • DOI: https://doi.org/10.1007/s11075-022-01321-y

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