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A modified proximal point algorithm for a nearly asymptotically quasi-nonexpansive mapping with an application

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Abstract

In this paper, we introduce a new modified proximal point algorithm based on M-iteration to approximate a common element of the set of solutions of convex minimization problems and the set of fixed points of nearly asymptotically quasi-nonexpansive mapping in CAT(0) space. We also prove the \(\Delta \)-convergence of the proposed algorithm for solving common minimization problem and fixed point problem. We also provide an application and numerical results based on our proposed algorithm.

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Acknowledgements

The first author is grateful to University Grants Commission, India for providing financial assistance in the form of Junior Research Fellowship. Authors are thankful to the anonymous referees for their critical comments and suggestions.

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This research received no external funding.

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Authors and Affiliations

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

    Sabiya Khatoon & Izhar Uddin

  2. Department of Mathematics, Faculty of Sciences and Arts, Sakarya University, Sakarya, Turkey

    Metin Basarir

Authors
  1. Sabiya Khatoon
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  2. Izhar Uddin
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  3. Metin Basarir
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The authors have contributed in this work on an equal basis. All authors read and approved the final manuscript.

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Correspondence to Izhar Uddin.

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Communicated by Orizon Pereira Ferreira.

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Khatoon, S., Uddin, I. & Basarir, M. A modified proximal point algorithm for a nearly asymptotically quasi-nonexpansive mapping with an application. Comp. Appl. Math. 40, 250 (2021). https://doi.org/10.1007/s40314-021-01646-9

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  • DOI: https://doi.org/10.1007/s40314-021-01646-9

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