Sadarangani, Fixed point theorems for weakly contractive mappings in

partially ordered sets, Nonlinear Anal.

The first result in this direction was given by Turinici [29], where he extended the Banach contraction principle in

partially ordered sets.

Rodriguez-Lopez, Contractive mapping theorems in

partially ordered sets and applications to ordinary differential equations, Order, 22(2005) 223-239.

Partially ordered sets (a special kind of DAG) are often used in mathematics to analyze ordering, sequencing or arrangement of distinct objects which can block all routes from the maximal to the minimal nodes by killing a subset of agents in a terror network.

Appendices review

partially ordered sets, Lebesgue measure theory, and mollifications.

Forbasic notions concerning

partially ordered sets (posets), see the book by Stanley [14].

Generally, the Cartesian product of two

partially ordered sets ([S.

Their topics include contraction mappings, fixed point theorems in

partially ordered sets, topological fixed point theorems, variational and quasivariational inequalities in topological vectors spaces and generalized games, best approximations and fixed point theorems for set-valued mappings in topological vector spaces, degree theories for set-valued mappings, and nonexpansive types of mappings and fixed-point theorems in locally convex topological vector spaces.

Among other things, this last realization shows us that

partially ordered sets can be treated as compositional designs.

Rodriguez-Lopez: Existence and uniqueness of fixed point in

partially ordered sets and applications to ordinary differenatial equations, Acta Math.

For more information on

partially ordered sets we refer the reader to [21, Chapter 3].

These proceedings from the August 2005 conference include both original research and survey articles, focusing on interactions of combinatories with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and

partially ordered sets.