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1.
Let f be a transcendental meromorphic function and g(z)=f(z+1)−f(z). A number of results are proved concerning the existences of zeros and fixed points of g(z) or g(z)/f(z) which expand results of Bergweiler and Langley [W. Bergweiler, J.K. Langley, Zeros of differences of meromorphic functions, Math. Proc. Cambridge Philos. Soc. 142 (2007) 133-147].  相似文献   

2.
In this paper, we prove the following strong convergence theorem: Let be a closed convex subset of a Hilbert space . Let be a strongly continuous semigroup of nonexpansive mappings on such that . Let and be sequences of real numbers satisfying , 0$"> and . Fix and define a sequence in by for . Then converges strongly to the element of nearest to .

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By considering bijections from the set of Dyck paths of length 2n onto each of Sn(321) and Sn(132), Elizalde and Pak in [S. Elizalde, I. Pak, Bijections for refined restricted permutations, J. Combin. Theory Ser. A 105 (2004) 207-219] gave a bijection that preserves the number of fixed points and the number of excedances in each σSn(321). We show that a direct bijection Γ:Sn(321)→Sn(132) introduced by Robertson in [A. Robertson, Restricted permutations from Catalan to Fine and back, Sém. Lothar. Combin. 50 (2004) B50g] also preserves the number of fixed points and the number of excedances in each σ. We also show that a bijection ?:Sn(213)→Sn(321) studied in [J. Backelin, J. West, G. Xin, Wilf-equivalence for singleton classes, Adv. in Appl. Math. 38 (2007) 133-148] and [M. Bousquet-Melou, E. Steingrimsson, Decreasing subsequences in permutations and Wilf equivalence for involutions, J. Algebraic Combin. 22 (2005) 383-409] preserves these same statistics, and we show that an analogous bijection from Sn(132) onto Sn(213) does the same.  相似文献   

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A word w is a fixed point of a nontrivial morphism h if w=h(w) and h is not the identity on the alphabet of w. The paper presents the first polynomial algorithm deciding whether a given finite word is such a fixed point. The algorithm also constructs the corresponding morphism, which has the smallest possible number of non-erased letters.  相似文献   

7.
In a previous paper, we had proved that the permutation group generated by the round functions of an AES-like cipher is primitive. Here we apply the O’Nan Scott classification of primitive groups to prove that this group is the alternating group.   相似文献   

8.
We first prove characterizations of common fixed points of one-parameter nonexpansive semigroups. We next present convergence theorems to common fixed points.  相似文献   

9.
In this paper, we deal with a class of semilinear elliptic equations in a bounded domain , , with boundary. Using a new fixed point result of the Krasnoselskii type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.

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10.
W.A. Kirk [J. Math. Anal. Appl. 277 (2003) 645-650] first introduced the notion of asymptotic contractions and proved the fixed point theorem for this class of mappings. In this note we present a new short and simple proof of Kirk's theorem.  相似文献   

11.
本证明了半度量空间中的Ekeland变分原理及Caristic不动点定理.进而证明了半度量空间中的压缩映像原理。  相似文献   

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Given any two positive integers k and n, this paper is concerned with the existence of a circle action on a closed, smooth orientable n-dimensional manifold with precisely k isolated fixed points. We first show that this existence problem can be reduced to that of an n-dimensional manifold with exactly three fixed points. Then by using a rigidity result, we determine possible weights on these three fixed points when n = 4.  相似文献   

14.
This paper considers existence of multiple positive fixed points for some nonlinear operators, a particular case of the operators is sum of an e-concave operator and an e-convex operator. Then we apply the results to nonlinear integral equations.  相似文献   

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In this paper we study the regularity of geodesic Ptolemy spaces and apply our findings to metric fixed point theory. It is an open question whether such spaces with a continuous midpoint map are CAT(0) spaces. We prove that if a certain uniform continuity is imposed on such a midpoint map then these spaces, if complete, are reflexive (that is, the intersection of decreasing families of bounded closed and convex subsets is nonempty) and that bounded sequences have unique asymptotic centers. These properties will then be applied to yield a series of fixed point results specific to CAT(0) spaces.  相似文献   

18.
Let f be a nonconstant entire function, and let k (?2) be an integer. We denote by the set consisting of all the fixed points of f. This paper proves that if f and f′ have the same fixed points, namely, Ef(z)=Ef(z), and if f(k)(z)=z whenever f(z)=z, then ff′.  相似文献   

19.
Let f: (X, A)→(X, A) be an admissible selfmap of a pair of metrizable ANR's. A Nielsen number of the complement Ñ(f; X, A) and a Nielsen number of the boundary ñ(f; X, A) are defined. Ñ(f; X, A) is a lower bound for the number of fixed points on C1(X - A) for all maps in the homotopy class of f. It is usually possible to homotope f to a map which is fixed point free on Bd A, but maps in the homotopy class of f which have a minimal fixed point set on X must have at least ñ(f; X, A) fixed points on Bd A. It is shown that for many pairs of compact polyhedra these lower bounds are the best possible ones, as there exists a map homotopic to f with a minimal fixed point set on X which has exactly Ñ(f; X - A) fixed points on C1(XA) and ñ(f; X, A) fixed points on Bd A. These results, which make the location of fixed points on pairs of spaces more precise, sharpen previous ones which show that the relative Nielsen number N(f; X, A) is the minimum number of fixed points on all of X for selfmaps of (X, A), as well as results which use Lefschetz fixed point theory to find sufficient conditions for the existence of one fixed point on C1(XA).  相似文献   

20.
The existence of coincidence and fixed points for continuous mappings on pseudo-compact completely regular topological spaces are proved. Our results are different from known, or are generalizations, extensions and improvements of the corresponding results due to Jungck, Liu and Liu et al. Further, the Edelstein result for contractive mappings is extended to Hausdorff (not necessarily completely regular) topological spaces and generalized in many aspects. An example is presented to show that our results are genuine generalizations of the Edelstein result.  相似文献   

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