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A new shrinking projection algorithm for a generalized mixed variational-like inequality problem and asymptotically quasi-\(\phi \)-nonexpansive mapping in a Banach space

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We propose and analyze a new inertial type iterative algorithm for finding a common solution of generalized mixed variational-like inequality problem, variational inequality problem for a \(\gamma \)-inverse strongly monotone mapping and fixed point problem for a asymptotically quasi-\(\phi \)-nonexpansive mapping in the framework of two-uniformly convex and uniformly smooth real Banach space. Further, we prove that the sequence generated by the proposed iterative algorithm converges strongly to a common solution of these problems. Furthermore, we give some consequences of the main result. Finally, we discuss some numerical examples to demonstrate the applicability of the iterative algorithm. The results presented in this paper unify and extend some known results in this area.

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Acknowledgements

The authors sincerely thank the reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original manuscript. W. Cholamjiak would like to thank University of Phayao, Phayao, Thailand and Thailand Science Research and Innovation under the project IRN62W0007.

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Authors and Affiliations

  1. Department of Mathematics, Deanship of Educational Services, Qassim University, Buraidah, 51452, Saudi Arabia

    Mohammad Farid

  2. School of Science, University of Phayao, Phayao, 56000, Thailand

    Watcharaporn Cholamjiak

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

    Rehan Ali

  4. Department of Mathematics, Faculty of Science and Arts- Rabigh, King Abdulaziz University, P.O. Box 344, Rabigh, 21911, Kingdom of Saudi Arabia

    K. R. Kazmi

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

    K. R. Kazmi

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  1. Mohammad Farid
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  2. Watcharaporn Cholamjiak
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  3. Rehan Ali
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  4. K. R. Kazmi
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All authors contributed equally and significantly in writing this paper. All authors read and approved the final manuscript.

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Correspondence to Mohammad Farid.

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Farid, M., Cholamjiak, W., Ali, R. et al. A new shrinking projection algorithm for a generalized mixed variational-like inequality problem and asymptotically quasi-\(\phi \)-nonexpansive mapping in a Banach space. RACSAM 115, 114 (2021). https://doi.org/10.1007/s13398-021-01049-9

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  • DOI: https://doi.org/10.1007/s13398-021-01049-9

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