Common fixed points and convergence results for $ \alpha $-Krasnosel'skii mappings

Amit Gangwar; Anita Tomar; Mohammad Sajid; R.C. Dimri; Amit Gangwar; Anita Tomar; Mohammad Sajid; R.C. Dimri

doi:10.3934/math.2023501

AIMS Mathematics

2023, Volume 8, Issue 4: 9911-9923. doi: 10.3934/math.2023501

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Research article

Common fixed points and convergence results for $ \alpha $-Krasnosel'skii mappings

1.
H.N.B. Garhwal University, Srinagar-246174, Uttarakhand, India
2.
Pt. L.M.S. Campus, Sridev Suman Uttarakhand University, Rishikesh-249201, Uttarakhand, India
3.
Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia

Received: 09 January 2023 Revised: 15 February 2023 Accepted: 16 February 2023 Published: 23 February 2023
MSC : 47H09, 47H10

We present convergence and common fixed point conclusions of the Krasnosel'skii iteration which is one of the iterative methods associated with $ \alpha $-Krasnosel'skii mappings satisfying condition (E). Our conclusions extend, generalize and improve numerous conclusions existing in the literature. Examples are given to support our results.
- $ \alpha $-Krasnosel'skii iteration,
- approximation,
- asymptotically regular,
- iterative methods,
- metric projection,
- Schauder theorem,
- uniformly convex Banach space
Citation: Amit Gangwar, Anita Tomar, Mohammad Sajid, R.C. Dimri. Common fixed points and convergence results for $ \alpha $-Krasnosel'skii mappings[J]. AIMS Mathematics, 2023, 8(4): 9911-9923. doi: 10.3934/math.2023501

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Abstract

We present convergence and common fixed point conclusions of the Krasnosel'skii iteration which is one of the iterative methods associated with $ \alpha $-Krasnosel'skii mappings satisfying condition (E). Our conclusions extend, generalize and improve numerous conclusions existing in the literature. Examples are given to support our results.

References

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