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Compact widths in metric trees

Asuman Güven Aksoy, Kyle Edward Kinneberg (2011)

Banach Center Publications

The definition of n-width of a bounded subset A in a normed linear space X is based on the existence of n-dimensional subspaces. Although the concept of an n-dimensional subspace is not available for metric trees, in this paper, using the properties of convex and compact subsets, we present a notion of n-widths for a metric tree, called Tn-widths. Later we discuss properties of Tn-widths, and show that the compact width is attained. A relationship between the compact widths and Tn-widths is also...

Compactness and convergence of set-valued measures

Kenny Koffi Siggini (2009)

Colloquium Mathematicae

We prove criteria for relative compactness in the space of set-valued measures whose values are compact convex sets in a Banach space, and we generalize to set-valued measures the famous theorem of Dieudonné on convergence of real non-negative regular measures.

Compatible mappings of type (B) and common fixed point theorems in Saks spaces

H. K. Pathak, M. S. Khan (1999)

Czechoslovak Mathematical Journal

In this paper we first introduce the concept of compatible mappings of type (B) and compare these mappings with compatible mappings and compatible mappings of type (A) in Saks spaces. In the sequel, we derive some relations between these mappings. Secondly, we prove a coincidence point theorem and common fixed point theorem for compatible mappings of type (B) in Saks spaces.

Compatible mappings of type ( β ) and weak compatibility in fuzzy metric spaces

Shobha Jain, Shishir Jain, Lal Bahadur Jain (2009)

Mathematica Bohemica

The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a generalized contractive condition through compatibility of type ( β ) and weak compatibility in a fuzzy metric space. It significantly generalizes the result of Singh and Jain [The Journal of Fuzzy Mathematics ( 2006 ) ] and Sharma [Fuzzy Sets and Systems ( 2002 ) ] . An example has been constructed in support of our main result. All the results presented in this paper are new.

Complementarities and the existence of strong Berge equilibrium

Kerim Keskin, H. Çağrı Sağlam (2014)

RAIRO - Operations Research - Recherche Opérationnelle

This paper studies the existence and the order structure of strong Berge equilibrium, a refinement of Nash equilibrium, for games with strategic complementarities à la strong Berge. It is shown that the equilibrium set is a nonempty complete lattice. Moreover, we provide a monotone comparative statics result such that the greatest and the lowest equilibria are increasing.

Completely generalized nonlinear variational inclusions for fuzzy mappings

Nan-jing Huang (1999)

Czechoslovak Mathematical Journal

In this paper, we introduce and study a new class of completely generalized nonlinear variational inclusions for fuzzy mappings and construct some new iterative algorithms. We prove the existence of solutions for this kind of completely generalized nonlinear variational inclusions and the convergence of iterative sequences generated by the algorithms.

Complexifications of real Banach spaces, polynomials and multilinear maps

Gustavo Muñoz, Yannis Sarantopoulos, Andrew Tonge (1999)

Studia Mathematica

We give a unified treatment of procedures for complexifying real Banach spaces. These include several approaches used in the past. We obtain best possible results for comparison of the norms of real polynomials and multilinear mappings with the norms of their complex extensions. These estimates provide generalizations and show sharpness of previously obtained inequalities.

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