Splitting type viscosity methods for inclusion and fixed point problems on Hadamard manifolds

Mohammad Dilshad; Aysha Khan; Mohammad Akram; Mohammad Dilshad; Aysha Khan; Mohammad Akram

doi:10.3934/math.2021309

AIMS Mathematics

2021, Volume 6, Issue 5: 5205-5221. doi: 10.3934/math.2021309

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Research article

Splitting type viscosity methods for inclusion and fixed point problems on Hadamard manifolds

1.
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, KSA
2.
Department of Mathematics, College of Arts and Science, Wadi-Ad-Dwasir, Prince Sattam bin Abdulaziz University, Al-Khraj, KSA
3.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah-170, KSA

Received: 03 October 2020 Accepted: 01 March 2021 Published: 11 March 2021
MSC : 47J20, 47J25, 49J40, 47H10

In this article, we suggest and analyze the splitting type viscosity methods for inclusion and fixed point problem of a nonexpansive mapping in the setting of Hadamard manifolds. We derive the convergence of sequences generated by the proposed iterative methods under some suitable assumptions. Several special cases of the proposed iterative methods are also discussed. Finally, some applications to solve the variational inequality, optimization and fixed point problems are given on Hadamard manifolds.
- splitting type viscosity method,
- variational inclusion,
- fixed point problem,
- nonexpansive mapping,
- variational inquality,
- Hadamard manifold
Citation: Mohammad Dilshad, Aysha Khan, Mohammad Akram. Splitting type viscosity methods for inclusion and fixed point problems on Hadamard manifolds[J]. AIMS Mathematics, 2021, 6(5): 5205-5221. doi: 10.3934/math.2021309

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Abstract

In this article, we suggest and analyze the splitting type viscosity methods for inclusion and fixed point problem of a nonexpansive mapping in the setting of Hadamard manifolds. We derive the convergence of sequences generated by the proposed iterative methods under some suitable assumptions. Several special cases of the proposed iterative methods are also discussed. Finally, some applications to solve the variational inequality, optimization and fixed point problems are given on Hadamard manifolds.

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