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On constrained minimization, variational inequality and split feasibility problem via new iteration scheme in Banach spaces

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Abstract

The motive of this paper is to propose a new iterative algorithm for evaluating a solution of constrained minimization problem, variational inequality and split feasibility problem and common fixed point of two generalized \(\alpha \)-nonexpansive mappings. We obtain few convergence results in the setting of uniformly convex Banach space. We also present some numerical examples for supporting our main results and to demonstrate the convergence behaviour of the obtained process.

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Acknowledgements

The authors are very grateful to the anonymous referees for pointing out the mistake in Lemma 3.2 and for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110025, India

    Chanchal Garodia & Izhar Uddin

  2. Department of Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

  4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Dumitru Baleanu

Authors
  1. Chanchal Garodia
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  2. Izhar Uddin
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  3. Dumitru Baleanu
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The authors gave equal contribution in this work. All authors read and approved the final manuscript.

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Correspondence to Izhar Uddin.

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The authors declare that they have no competing interests.

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Communicated by Hossein Mohebi.

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Garodia, C., Uddin, I. & Baleanu, D. On constrained minimization, variational inequality and split feasibility problem via new iteration scheme in Banach spaces. Bull. Iran. Math. Soc. 48, 1493–1512 (2022). https://doi.org/10.1007/s41980-021-00596-6

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  • DOI: https://doi.org/10.1007/s41980-021-00596-6

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