Three-dimensional convexity and the fixed point property for nonexpansive mappings

Mazcuñán-Navarro, Eva M.

doi:10.1016/j.na.2008.10.101

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“…Some more recent progress on the investigation of the implicit and explicit schemes (1.4) and (1.5) can be found in [2,8,9,15,17,25,26].…”

Section: Introductionmentioning

confidence: 99%

Approximation of a common minimum-norm fixed point of a finite family of σ -asymptotically quasi-nonexpansive mappings with applications

Pathak¹,

Sahu²,

Cho³

2016

J. Nonlinear Sci. Appl.

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In this paper, we use the iterative method proposed by Zegeye and Shahzad [H. Zegeye, N. Shahzed, Fixed Point Theory Appl., 2013 (2013), 12 pages] which converges strongly to the common minimum-norm fixed point of a finite family of σ-asymptotically quasi-nonexpansive mappings. As consequence, convergence results to a common minimum-norm fixed point of a finite family of asymptotically nonexpansive mappings is proved. Our result generalize and improve a recent result of Zegeye and Shahzad [H. Zegeye, N. Shahzed, Fixed Point Theory Appl., 2013 (2013), 12 pages]. In the sequel, we apply our main result to find solution of minimizer of a continuously Frechet-differentiable convex functional which has the minimum norm in Hilbert spaces.

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“…Some more recent progress on the investigation of the implicit and explicit schemes (1.4) and (1.5) can be found in [2,8,9,15,17,25,26].…”

Section: Introductionmentioning

confidence: 99%