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Strict pseud-contraction strong convergence theorems for strict pseud-contractions

100%

Qin X. , Su Y.

tom Vol. 30

137-149

In this paper, we prove two strong convergence theorems for strict pseudocontractions in Hilbert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo and Takahashi [K. Nakajo, W. Takahashi,. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003), 372-379], Marino and Xu [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), 336-346], Martinez-Yanes and Xu [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anai. 64 (2006), 2400-2411] and some others.

On nonlinear differential equations in generalized Musielak-Orlicz spaces

84%

Kozlowski W. M.

tom Vol. 53, No. 2

13--33

We consider ordinary differential equations u′(t)+(I−T)u(t)=0, where an unknown function takes its values in a given modular function space being a generalization of Musielak-Orlicz spaces, and T is nonlinear mapping which is nonexpansive in the modular sense. We demonstrate that under certain natural assumptions the Cauchy problem related to this equation can be solved. We also show a process for the construction of such a solution. This result is then linked to the recent results of the fixed point theory in modular function spaces.

Structure of the fixed point set of asymptotically nonexpansive mappings in Banach spaces with weak uniformly normal structure

84%

Sahu D. R. , Agarwal R. P. , O'Regan D.

tom Vol. 17, nr 1

51-68

This paper is concerned with weak uniformly normal structure and the structure of the set of fixed points of Lipschitzian mappings. It is shown that in a Banach space X with weak uniformly normal structure, every asymptotically regular Lipschitzian semigroup of self-mappings defined on a weakly compact convex subset of X satisfies the (ω)-fixed point property. We show that if X has a uniformly Gâteaux differentiable norm, then the set of fixed points of every asymptotically nonexpansive mapping is nonempty and sunny nonexpansive retract of C. Our results improve several known fixed point theorems for the class of Lipschitzian mappings in a general Banach space.

Implicit and explicit constructions of sunny nonexpansive retractions in Banach spaces

67%

Aleyner A. , Reich S.

tom Vol. 29

5-16

Implicit and explicit processes for eonstructing the unique sunny nonexpansive retraction onto the common fixed point set of either a finite or infmite family of nonexpansive mappings in a Banach space are proposed and corresponding convergence theorems are established.