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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.

Continuous dependence on parameters of the fixed points set for some set-valued operators

Eduard Kirr, Adrian Petruel (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we extend the notion of I⁰-continuity and uniform I⁰-continuity from [2] to set-valued operators. Using these properties, we prove some results on continuous dependence of the fixed points set for families of contractive type set-valued operators.

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