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On enriched Hardy–Rogers contractions in Banach space via Krasnoselskij iteration with an application

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Abstract

In this paper we initiate the study of enriched Hardy–Rogers contraction in Banach space and utilize it to establish fixed point results by using the Krasnoselskij iteration scheme. Further, we provide illustrative examples to justify the obtained conclusions and demonstrate the remarkable fact that our novel enriched contractions need not be continuous. Lastly, we introduce the notion of enriched generalized Hardy–Rogers contraction and elaborate its application in finding local fixed points by using the significant fact that the iteration scheme doesn’t dislocate the centre of the open ball too far.

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Acknowledgements

The authors are thankful to the learned reviewer for his valuable comments.

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Authors declare that there is no funding available for this article.

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Authors and Affiliations

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

    Pragati Gautam, Swapnil Verma & Soumya Gulati

  2. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania

    Santosh Kumar

  3. Department of Mathematics, North-Eastern Hill University, Shillong, 793022, Meghalaya, India

    Santosh Kumar

Authors
  1. Pragati Gautam
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  2. Santosh Kumar
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  3. Swapnil Verma
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  4. Soumya Gulati
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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Correspondence to Santosh Kumar.

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Communicated by S Ponnusamy.

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Gautam, P., Kumar, S., Verma, S. et al. On enriched Hardy–Rogers contractions in Banach space via Krasnoselskij iteration with an application. J Anal 32, 1145–1160 (2024). https://doi.org/10.1007/s41478-023-00680-6

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  • DOI: https://doi.org/10.1007/s41478-023-00680-6

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