The Convergence of AA-Iterative Algorithm for Generalized AK-𝛼-Nonexpansive Mappings in Banach Spaces

Cholatis Suanoom; Anteneh Getachew  Gebrie; Thanatporn  Grace

The Convergence of AA-Iterative Algorithm for Generalized AK-𝛼-Nonexpansive Mappings in Banach Spaces

Authors

Cholatis Suanoom Program of Mathematics, Faculty of Science and Technology, Kamphaengphet Rajabhat University, Kamphaengphet 62000, Thailand
Anteneh Getachew Gebrie Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan 445, Ethiopia
Thanatporn Grace Mathematics English Program, Faculty of Education, Valaya Alongkorn Rajabhat University under the Royal Patronage, Pathum Thani 13180, Thailand

Keywords:

AK-𝛼-generalized nonexpansive mapping, Banach space, Convergence theorem, Fixed point, Hilbert space

Abstract

In this paper, we are inspired by the collective ideas of the authors mentioned, making us interested in studying about the strong and weak convergence results by using the AA-iterative algorithm (1.14) for the generalized AK-𝛼-nonexpansive mappings (1.5) in uniformly convex Banach spaces . In particular, we provide only sufficient convergence criteria for a suitable procedural method. Our work is more general and unifies the comparable results in the existing literature, for instance, the results given in [1].

References

Beg, I.; Abbas, M.; Asghar, M.W.Convergence of AA-Iterative Algorithm for Generalized α-Nonexpansive Mappings with an Application. Mathematics 2022, 10, 4375. https://doi.org/10.3390/math10224375

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Published

2023-09-26

How to Cite

Suanoom, C., Gebrie, A. G. ., & Grace, T. . (2023). The Convergence of AA-Iterative Algorithm for Generalized AK-𝛼-Nonexpansive Mappings in Banach Spaces. Science & Technology Asia, 28(3), 82–90. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/248796