共查询到20条相似文献,搜索用时 15 毫秒
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W. K. Min 《Acta Mathematica Hungarica》2009,124(1-2):73-81
We introduce the notions of weak (g, g′)-continuity and weak (ψ, ψ′)-continuity on GTS’s and GNS’s, respectively, and investigate characterizations for such functions and relationships between weak (g, g′)-continuity and weak (ψ, ψ′)-continuity. 相似文献
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M. S. Sarsak 《Acta Mathematica Hungarica》2011,131(1-2):110-121
We study a unified approach of weak separation axioms in generalized topological spaces. 相似文献
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Different generalizations of topological Baire spaces to the case of generalized topological spaces are considered and the properties of such spaces are examined. In particular, these considerations are focused on the relationship between Baire generalized topological spaces and semi-continuous real functions and infinite games. The notion of generalized metric spaces corresponding to generalized topological spaces is introduced as an important tool in this discussion. 相似文献
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Won Keun Min 《Acta Mathematica Hungarica》2005,108(1-2):171-181
Summary We characterize some properties of generalized topological spaces and (g,g’)-continuity by using an interior operator defined on a generalized topological space. Also, we introduce the notions of (ψ, ψ’)-open map, gn-continuity, gn-open map and investigate their properties by using new interior (or closure) operators defined on generalized neighborhood systems of a nonempty set. 相似文献
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Designs, Codes and Cryptography - This paper investigates the construction of $${\text {MDS}}$$ matrices with generalized Feistel structures ( $${\text {GFS}}$$ ). The approach developed by this... 相似文献
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M. Turinici 《Periodica Mathematica Hungarica》1982,13(3):259-264
In this note, some problems concerning existence of maximal elements in a topological as well as in a generalized metric space, equipped with an ordering, are studied. The results presented here may be considered as a partial refinement of those established in [2] for uniform structures. 相似文献
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T. A. Avakyan P. S. Gevorgyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(1):52-59
The paper is devoted to one of the important notions of the shape theory: that of strong movability, which was primarily introduced
by K. Borsuk for metrizable compacts. A strong movability criterion is proved for topological spaces, which in particular
reveals a new, categorical approach to the strong movability. 相似文献
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We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p > 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1<p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results. 相似文献
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Weak and strong convergence theorems are proved in real Hilbert spaces for a new class of nonspreading-type mappings more general than the class studied recently in Kurokawa and Takahashi [Y. Kurokawa, W. Takahashi, Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces, Nonlinear Anal. 73 (2010) 1562-1568]. We explored an auxiliary mapping in our theorems and proofs and this also yielded a strong convergence theorem of Halpern’s type for our class of mappings and hence resolved in the affirmative an open problem posed by Kurokawa and Takahashi in their final remark for the case where the mapping T is averaged. 相似文献
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对广义近似空间之间的映射引入并刻画了粗糙连续性和拓扑连续性,探讨了他们的性质及相互关系.证明了两个粗糙连续映射的复合还是粗糙连续的,每个粗糙连续的映射都是拓扑连续的.在此基础上引入了粗糙同胚性质和拓扑同胚性质的概念,证明了拓扑同胚性质均为粗糙同胚性质并考察了广义近似空间的诸如分离性、连通性、紧性等的粗糙同胚不变性和拓扑同胚不变性. 相似文献
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Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces 总被引:1,自引:0,他引:1
Giuseppe Marino 《Journal of Mathematical Analysis and Applications》2007,329(1):336-346
Let C be a closed convex subset of a real Hilbert space H and assume that T is a κ-strict pseudo-contraction on C with a fixed point, for some 0?κ<1. Given an initial guess x0∈C and given also a real sequence {αn} in (0,1). The Mann's algorithm generates a sequence {xn} by the formula: xn+1=αnxn+(1−αn)Txn, n?0. It is proved that if the control sequence {αn} is chosen so that κ<αn<1 and , then {xn} converges weakly to a fixed point of T. However this convergence is in general not strong. We then modify Mann's algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence. This result extends a recent result of Nakajo and Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379] from nonexpansive mappings to strict pseudo-contractions. 相似文献
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Yu Kurokawa 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1562-1822
In this paper, we first obtain a weak mean convergence theorem of Baillon’s type for nonspreading mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem for nonspreading mappings in a Hilbert space. 相似文献
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We present some criteria for the metrizability of a topological space in terms of weak base g-functions and with these criteria we improve some results on metrizability that appeared in literature. Moreover, we answer a question posed in Li (2008) [7]. 相似文献
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Pseudomonotone maps are a generalization of paramonotone maps which is very closely related to the cutting plane property in variational
inequality problems (VIP). In this paper, we first generalize the so-called minimum principle sufficiency and the maximum
principle sufficiency for VIP with multivalued maps. Then we show that pseudomonotonicity of the map implies the “maximum principle sufficiency” and, in fact, is equivalent to it in a sense. We then present two
applications of pseudomonotone maps. First we show that pseudomonotone maps can be used instead of the much more restricted class of pseudomonotone+ maps in a cutting plane method. Finally, an application to a proximal point method is given.
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