Modified inertial Ishikawa iterations for fixed points of nonexpansive mappings with an application

Hasanen A. Hammad; Hassan Almusawa; Hasanen A. Hammad; Hassan Almusawa

doi:10.3934/math.2022388

AIMS Mathematics

2022, Volume 7, Issue 4: 6984-7000. doi: 10.3934/math.2022388

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Research article

Modified inertial Ishikawa iterations for fixed points of nonexpansive mappings with an application

Hasanen A. Hammad ^{1
,
,},
Hassan Almusawa ²

1.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
2.
Department of Mathematics, College of Sciences, Jazan Univesity, Jazan 45142, Saudi Arabia

Received: 15 September 2021 Revised: 07 January 2022 Accepted: 17 January 2022 Published: 07 February 2022
MSC : 47H09, 47J25

This manuscript aims to prove that the sequence $ \{\nu _{n}\} $ created iteratively by a modified inertial Ishikawa algorithm converges strongly to a fixed point of a nonexpansive mapping $ Z $ in a real uniformly convex Banach space with uniformly Gâteaux differentiable norm. Moreover, zeros of accretive mappings are obtained as an application. Our results generalize and improve many previous results in this direction. Ultimately, two numerical experiments are given to illustrate the behavior of the purposed algorithm.
- nonexpansive mappings,
- accretive mappings,
- uniformly Gâteaux differentiable norm,
- evolution equations
Citation: Hasanen A. Hammad, Hassan Almusawa. Modified inertial Ishikawa iterations for fixed points of nonexpansive mappings with an application[J]. AIMS Mathematics, 2022, 7(4): 6984-7000. doi: 10.3934/math.2022388

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Abstract

This manuscript aims to prove that the sequence $ \{\nu _{n}\} $ created iteratively by a modified inertial Ishikawa algorithm converges strongly to a fixed point of a nonexpansive mapping $ Z $ in a real uniformly convex Banach space with uniformly Gâteaux differentiable norm. Moreover, zeros of accretive mappings are obtained as an application. Our results generalize and improve many previous results in this direction. Ultimately, two numerical experiments are given to illustrate the behavior of the purposed algorithm.

References

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