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A Novel Iterative Scheme To Approximate the Fixed Points of Zamfirescu Operator and Generalized Non-Expansive Map with an Application

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Abstract

This paper aims at defining a novel and a faster iterative scheme called PC-iterative scheme to approximate the fixed points of the Zamfirescu operator and Generalized non-expansive mapping. The weak and strong convergence and stability results are established. It is justified numerically that the PC-iterative scheme converges faster than many other known iterative schemes due to Agarwal et al. [9], Gursoy et al. [11], Thakur et al. [5], and F. Ali et al. [14]. Functional differential equations have their application in more realistic mathematical models which depends on the history of the system. Hence functional differential is more significant due to their ease of applicability in real-world problems than Ordinary differential equations. As an application of the PC-iterative scheme, we will obtain the solution of a functional differential equation. To support the validity of our results, examples with graphical representations are provided using Python programming.

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Authors and Affiliations

  1. Kamala Nehru College, University of Delhi, August Kranti Marg, 110049, New Delhi, India

    Pragati Gautam

  2. Janki Devi Memorial College, University of Delhi, Sir Ganga Ram Hospital Marg, 110060, New Delhi, India

    Chanpreet Kaur

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  1. Pragati Gautam
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  2. Chanpreet Kaur
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Correspondence to Pragati Gautam or Chanpreet Kaur.

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(Submitted by A. M. Elizarov)

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Gautam, P., Kaur, C. A Novel Iterative Scheme To Approximate the Fixed Points of Zamfirescu Operator and Generalized Non-Expansive Map with an Application. Lobachevskii J Math 44, 1316–1331 (2023). https://doi.org/10.1134/S1995080223040108

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  • DOI: https://doi.org/10.1134/S1995080223040108

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