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The Second Moments for Meyer-K(o)nig and Zeller Operators on a Simplex
单纯形上Meyer Konig and Zeller算子的二阶矩量 [DM)]

ZHANG Chun-Gou,
张春苟

数学物理学报(A辑) , 2005,
Abstract: 该文讨论了单纯形上Meyer—Konig and Zeller算子的矩量问题.首先得到了二阶矩量在广义积分下的显式表示,并由此导出了二阶矩量的二元Appell超几何函数表示。超几何级数表示和完全渐近公式.
Generating functions for q-Bernstein, q-Meyer-Konig-Zeller and q-Beta basis  [PDF]
Vijay Gupta,Taekyun Kim,Jongsung Choi,Young-Hee Kim
Mathematics , 2010,
Abstract: The present paper deals with the q-analogue of Bernstein, Meyer-Konig-Zeller and Beta operators. Here we estimate the generating functions for q-Bernstein, q-Meyer-Konig-Zeller and q-Beta basis functions.
A note on integral modification of the Meyer-K?nig and Zeller operators
Vijay Gupta,Niraj Kumar
International Journal of Mathematics and Mathematical Sciences , 2003, DOI: 10.1155/s0161171203208218
Abstract: Guo (1988) introduced the integral modification of Meyer-Kö nig and Zeller operators Mˆn and studied the rate of convergence for functions of bounded variation. Gupta (1995) gave the sharp estimate for the operators Mˆn. Zeng (1998) gave the exact bound and claimed to improve the results of Guo and Gupta, but there is a major mistake in the paper of Zeng. In the present note, we give the correct estimate for the rate of convergence on bounded variation functions.
On strong approximation by modified Meyer-K"onig and Zeller operators
L. Rempulska,M. Skorupka
Tamkang Journal of Mathematics , 2006, DOI: 10.5556/j.tkjm.37.2006.123-130
Abstract: We introduce certain modified Meyer-K"onig and Zeller operators $ M_{n;r} $ in the space of $r $-th times differentiable functions $ f $ and we study strong differences $ H_{n;r}^q(f) $ for them. This note is motivated by results on strong approximation connected with Fourier series ([7]).
Exact bounds for some basis functions of approximation operators
Zeng Xiao-Ming,Zhao Jun-Ning
Journal of Inequalities and Applications , 2001,
Abstract: The exact bounds of Bernstein basic functions and Meyer-Konig and Zeller basis functions have been determined in [J. Math. Anal. Appl., 219 (1998), 364–376]. In this note the exact bounds of some other basis functions of approximation operators and corresponding probability distributions are determined.
Critical independent sets and Konig--Egervary graphs  [PDF]
Vadim E. Levit,Eugen Mandrescu
Computer Science , 2009,
Abstract: Let alpha(G) be the cardinality of a independence set of maximum size in the graph G, while mu(G) is the size of a maximum matching. G is a Konig--Egervary graph if its order equals alpha(G) + mu(G). The set core(G) is the intersection of all maximum independent sets of G (Levit & Mandrescu, 2002). The number def(G)=|V(G)|-2*mu(G) is the deficiency of G (Lovasz & Plummer, 1986). The number d(G)=max{|S|-|N(S)|:S in Ind(G)} is the critical difference of G. An independent set A is critical if |A|-|N(A)|=d(G), where N(S) is the neighborhood of S (Zhang, 1990). In 2009, Larson showed that G is Konig--Egervary graph if and only if there exists a maximum independent set that is critical as well. In this paper we prove that: (i) d(G)=|core(G)|-|N(core(G))|=alpha(G)-mu(G)=def(G) for every Konig--Egervary graph G; (ii) G is Konig--Egervary graph if and only if every maximum independent set of G is critical.
On Konig-Egervary Square-Stable Graphs  [PDF]
Vadim E. Levit,Eugen Mandrescu
Computer Science , 2009,
Abstract: The stability number of a graph G, denoted by alpha(G), is the cardinality of a maximum stable set, and mu(G) is the cardinality of a maximum matching in G. If alpha(G)+mu(G) equals its order, then G is a Konig-Egervary graph. In this paper we deal with square-stable graphs, i.e., the graphs G enjoying the equality alpha(G)=alpha(G^{2}), where G^{2} denotes the second power of G. In particular, we show that a Konig-Egervary graph is square-stable if and only if it has a perfect matching consisting of pendant edges, and in consequence, we deduce that well-covered trees are exactly the square-stable trees.
A tree version of Konig's theorem  [PDF]
Ron Aharoni,Eli Berger,Ran Ziv
Mathematics , 1999,
Abstract: Konig's theorem states that the covering number and the matching number of a bipartite graph are equal. We prove a generalisation of this result, in which each point in one side of the graph is replaced by a subtree of a given tree. The proof uses a recent extension of Hall's theorem to families of hypergraphs, by the first author and P. Haxell.
On a theorem of W. Meyer-K?nig and H. Tietz
Brah m anak,Mehmet D k,F l z D k
International Journal of Mathematics and Mathematical Sciences , 2005, DOI: 10.1155/ijmms.2005.2491
Abstract: Let (un) be a sequence of real numbers and let L be an additive limitable method with some property. We prove that if the classical control modulo of the oscillatory behavior of (un) belonging to some class of sequences is a Tauberian condition for L, then convergence or subsequential convergence of (un) out of L is recovered depending on the conditions on the general control modulo of the oscillatory behavior of different order.
Deforming Meyer sets  [PDF]
Jeong-Yup Lee,Robert V. Moody
Mathematics , 2009, DOI: 10.1016/j.ejc.2008.01.016
Abstract: A linear deformation of a Meyer set $M$ in $\RR^d$ is the image of $M$ under a group homomorphism of the group $[M]$ generated by $M$ into $\RR^d$. We provide a necessary and sufficient condition for such a deformation to be a Meyer set. In the case that the deformation is a Meyer set and the deformation is injective, the deformation is pure point diffractive if the orginal set $M$ is pure point diffractive.
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