On fixed point results for some generalized nonexpansive mappings

Buthinah A. Bin Dehaish; Rawan K. Alharbi; Buthinah A. Bin Dehaish; Rawan K. Alharbi

doi:10.3934/math.2023290

AIMS Mathematics

2023, Volume 8, Issue 3: 5763-5778. doi: 10.3934/math.2023290

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Research article

On fixed point results for some generalized nonexpansive mappings

Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia

Received: 23 June 2022 Revised: 30 November 2022 Accepted: 04 December 2022 Published: 23 December 2022
MSC : 47H10, 54H25

We investigate an Ishikawa iteration process in the set up of generalized $ \alpha $- nonexpansive mappings. Approximation of these two mappings to a common fixed point by $ \Delta- $convergence and strong convergence of the scheme in hyperbolic space are also illustrated. The presented results amplify and polish many recent ideas put forward in uniformly convex Banach spaces, including CAT(0) spaces.
- common fixed point,
- generalized $ \alpha $- nonexpansive mappings,
- hyperbolic space
Citation: Buthinah A. Bin Dehaish, Rawan K. Alharbi. On fixed point results for some generalized nonexpansive mappings[J]. AIMS Mathematics, 2023, 8(3): 5763-5778. doi: 10.3934/math.2023290

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Abstract

We investigate an Ishikawa iteration process in the set up of generalized $ \alpha $- nonexpansive mappings. Approximation of these two mappings to a common fixed point by $ \Delta- $convergence and strong convergence of the scheme in hyperbolic space are also illustrated. The presented results amplify and polish many recent ideas put forward in uniformly convex Banach spaces, including CAT(0) spaces.

References

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