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An inertial-viscosity algorithm for solving split generalized equilibrium problem and a system of demimetric mappings in Hilbert spaces

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Abstract

In this paper, we introduce a new inertial-viscosity approximation method for solving a split generalized equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm is designed such that its convergence does not require the norm of the bounded linear operator underlying the split equilibrium problem. Moreover, a strong convergence result is proved under mild conditions in real Hilbert spaces. Furthermore, we give some numerical examples to show the efficiency and accuracy of the proposed method and we also compare the performance of our algorithm with other related methods in the literature.

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Acknowledgements

This paper was completed when L.O was visiting the Federal University of Agriculture, Abeokuta (FUNAAB). The author thanks the institution for providing their resources for the research.

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Authors and Affiliations

  1. Sefako Makgatho Health Sciences University, Ga-Rankuwa, P.O. Box 60, Pretoria, 0204, South Africa

    Maggie Aphane, Lateef Olakunle Jolaoso & Kazeem Olalekan Aremu

  2. Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun state, Nigeria

    Lateef Olakunle Jolaoso

  3. Department of Mathematics, Usmanu Danfodiyo University Sokoto, Sokoto, Sokoto state, Nigeria

    Kazeem Olalekan Aremu

  4. Department of Mathematics, The Technion – Israel Institute of Technology, Haifa, Israel

    Olawale Kazeem Oyewole

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  1. Maggie Aphane
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  2. Lateef Olakunle Jolaoso
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  3. Kazeem Olalekan Aremu
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  4. Olawale Kazeem Oyewole
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All authors worked equally on the results and approved the final manuscript.

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Correspondence to Olawale Kazeem Oyewole.

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Aphane, M., Jolaoso, L.O., Aremu, K.O. et al. An inertial-viscosity algorithm for solving split generalized equilibrium problem and a system of demimetric mappings in Hilbert spaces. Rend. Circ. Mat. Palermo, II. Ser 72, 1599–1628 (2023). https://doi.org/10.1007/s12215-022-00761-8

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