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Estimation of common fixed points of SKC mappings and an application to fractional differential equations

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Abstract

This article aims to show that the classes of enriched nonexpansive mappings due to Berinde, the mappings satisfying Suzuki-(KC)-condition due to Karapinar and Taş and generalized nonexpansive mappings due to Hardy and Rogers do not imply each other. As an application of our main results, a common solution of the nonlinear fractional differential equations is approximated. Further, we establish some weak and strong convergence results for two Suzuki-(KC) mappings to approximate common fixed points by using S-type iterative algorithm in uniformly convex Banach spaces. For the valuation of our results, a couple of nontrivial numerical examples are also presented.

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Acknowledgements

The authors are thankful to the learned referee for the comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Javid Ali & Mohd Jubair

  2. Department of Mathematics, National Institute of Technology, Jalandhar, India

    Mohd Jubair

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  1. Javid Ali
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  2. Mohd Jubair
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Correspondence to Javid Ali.

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Communicated by S. Ponnusamy.

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Ali, J., Jubair, M. Estimation of common fixed points of SKC mappings and an application to fractional differential equations. J Anal 32, 889–913 (2024). https://doi.org/10.1007/s41478-023-00662-8

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