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Finally, we present a case study with novel fMRI data in the domain of rule representations, or flexible stimulus response mappings, which has seen several recent MVPA publications.

So the class of mappings which has condition ((C)) is broader than the class of nonexpansive mappings.

In 1938, Ostrowski [2] established an interesting integral inequality associated with differentiable mappings which has powerful applications in numerical integration, probability and optimization theory, stochastic, statistics, information and integral operator theory.

Next, we consider a special type of mappings which has been used by number of authors in the fields of variational inequality theory and complementarity theory (see [4 6]).

The techniques for proving the existence of equilibrium have been used to solve a new type of systems of quasi-variational inequalities with random fuzzy mappings which has been introduced in a special section.

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Maps between circle packings with the same tangency are discrete analogues of conformal mappings, which have application for example in mechanical, fluid, and thermal engineering.

Nonexpansive mappings are those mappings which have Lipschitz constant equal to one.

There exist mappings which have only confined singularities and which are not integrable [15].

Concrete examples of maximalizing mappings which have or do not have fixed points are presented.

Weak contractions (also called ϕ-contractions) are generalizations of Banach contraction mappings which have been studied by several authors.

In this section, we first recall several generalizations of nonexpansive mappings, which have been introduced in recent years.

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