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On equality in an upper bound for the acyclic domination number

Samodivkin V.

Opuscula Mathematica

2008

Vol. 28, no. 3

331-334

A subset A of vertices in a graph G is acyclic if the subgraph it induces contains no cycles. The acyclic domination number ϒa (G) of a graph G is the minimum cardinality of an acyclic dominating set of G. For any graph G with n vertices and maximum degree Δ(G), ϒa(G) ≤ n - Δ(G). In this paper we characterize the connected graphs and the connected triangle-free graphs which achieve this upper bound.

On minimax inequalities in topological spaces without convexity structure

Lu H.-S.

Journal of Applied Analysis

2007

Vol. 13, nr 1

133-149

In this paper, we give a new nonempty intersection theorem in general topological spaces without convexity structure. As its applications, some new minimax inequalities are obtained in general topological spaces without convexity structure.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

Wu X., Thompson B., Yuan X.

Journal of Applied Analysis

2003

Vol. 9, nr 2

249-260

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study fixed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

A new generalization of browder fixed point theorem with applications

Wu X., Xu Y.

Journal of Applied Analysis

1998

Vol. 4, nr 2

205-214

In the present paper, a new generalization of Browder fixed point theorem is obtained. As its applications, we obtain some generalized versions of Browder's theorems for quasivariational inequality and Ky Fan's minimax inequality and minimax principle.