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DOI: 10.23952/jnfa.2025.34
Received March 7, 2025; Accepted October 1, 2025; Published October 29, 2025
Abstract. The Mann algorithm has been extensively studied as one of the most fundamental iterative schemes designed to find a fixed point of an averaged operator. In this paper, we aim to develop a new parallel algorithm improving the Mann algorithm with double inertial extrapolations to find a common fixed point of a finite family of nonexpansive mappings. Our proposed algorithm allows iterations to be carried out simultaneously. We prove the weak convergence under suitable conditions, and we give an example in infinite-dimensional spaces. Finally, we apply our algorithm in the context of image restoration to deblur images without prior knowledge of the blurring operator.
How to Cite this Article:
P. Inkrong, P. Paimsang, P. Cholamjiak, Y. Savoye, W. Cholamjiak, Parallel double inertial Mann-type algorithm for blind image deblurring, J. Nonlinear Funct. Anal. 2025 (2025) 34.