# Flat convergence for integral currents in metric spaces

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We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the...

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The purpose of this paper is to study the existence of zero points for set-valued pseudomonotone operators in a Banach space by using a new condition which was recently proposed by the authors (Matsushita and Takahashi, Set-Valued Analysis 15:251ï¿½264, 2007).

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We characterize a nonlinear full invariant of compact Banach-space maps: Let ( X, ?.?) and ( Y, ?.?) be two Banach spaces and P C( X, Y) be all compact maps which map ( X, ?.?) to ( Y, ?.?). Then each weak operator-topology subseries-convergent series ? i P i in P c( X, Y) is also...

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The main results of the paper include (a) a theorem containing estimates for the surjection modulus of a â€œpartial compositionâ€ of set-valued mappings between metric spaces which contains as a particlar case well-known Milyutinâ€™s theorem about additive perturbation of a mapping...

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Let X be an arbitrary (real or complex) Banach space, endowed with the norm |.|. Consider the space of the continuous functions C ([0; T] ; X) (T > 0), endowed with the usual topology, and let M be a closed subset of it. One proves that each operator A : M â†’ M fullling for all x, y...

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Abstract??We consider the following implicit quasi-variational inequality problem: given two topological vector spacesEandF, two nonempty setsX$$\sqsubseteq$$EandC$$\sqsubseteq$$F, two multifunctions ? :?X? 2Xand ? :X? 2C, and a single-valued map?:$$x\times c\times x\to ir$$, find a pair$$(\hat...

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This paper proves the existence and uniqueness of solutions in a Banach space for the generalized stochastic Ginzburg-Landau equation with a multiplicative noise in two spatial dimensions. The noise is white in time and correlated in spatial variables. The condition on the parameters is the same...

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We study the extension of isometries between the unit spheres of quasi-Banach spaces L p for 0 < p < 1. We give some sufficient conditions such that an isometric mapping from the the unit sphere of L p( ï¿½) into that of another L p( ?) can be extended to be a linear isometry defined on the...

- CONVERGENCE THEOREMS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES. Yongfu Su; Xiaolong Qin; Meijuan Shang // Acta Mathematica Universitatis Comenianae;2008, Vol. 77 Issue 1, p31
Let E be a uniformly convex Banach space, and let K be a nonempty convex closed subset which is also a nonexpansive retract of E. Let T : K ? E be an asymptotically nonexpansive P mapping with {kn} ? [1,8) such that ?n=18(kn -1) < 8 and let F(T) be nonempty, where F(T) denotes the fixed points...