Chain-complete posets and directed sets with applications

George Markowsky

doi:10.1007/bf02485815

Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets

Abstract and Applied Analysis ◽

10.1155/2014/580621 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Jinlu Li ◽

Ying Liu ◽

Hongya Gao

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Topological Structure ◽

Fixed Point Theorems ◽

Equilibrium Problems ◽

Saddle Points ◽

Order Relation ◽

Partial Order Relation ◽

Chain Complete ◽

Set Valued Mappings

We apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure.

Download Full-text

GAP SEQUENCES OF GRAPH-DIRECTED SETS

Fractals ◽

10.1142/s0218348x16500365 ◽

2016 ◽

Vol 24 (03) ◽

pp. 1650036

Author(s):

JUAN DENG ◽

LIFENG XI

Keyword(s):

Separation Condition ◽

Interesting Application ◽

Strong Separation ◽

Self Similar ◽

Strong Separation Condition ◽

Directed Sets ◽

Gap Sequences

This paper studies the gap sequences of graph-directed sets satisfying the strong separation condition. An interesting application is to investigate the gap sequences of self-similar sets with overlaps.

Download Full-text

The Turbocharger Products and Manufacturing Research

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.651-653.932 ◽

2014 ◽

Vol 651-653 ◽

pp. 932-935

Author(s):

Su Ying Xu

Keyword(s):

Internal Combustion Engine ◽

Manufacturing Industry ◽

Combustion Engine ◽

Enterprise Management ◽

Production Scale ◽

Industry Chain ◽

Industrial Chain ◽

Mode Of Operation ◽

Chain Complete ◽

Production Organization

the exhaust turbine supercharger in the process of manufacturing is made up of many enterprises to participate in the production and management. Production organization form of the differences is determined by the scale of production and mode of operation. Parts of casting blank and parts processing has formed a complete industrial chain. Complete parts processing and manufacturing industry chain has failed to form the advantage of the products. Many companies, management can not meet the user's demand. Also can't satisfy the hosts, scale and qualification requirements of production enterprises. Enterprise management has been formed a consortium. Enterprise production scale and qualification of such as to meet the requirement of enterprises for internal combustion engine accessories. The manufacture of parts and exhaust turbocharger parts processing and assembly in production process can be controlled. Is helpful to the enterprise's development and improvement of product quality.

Download Full-text

Three counterexamples concerning ω-chain completeness and fixed point properties

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500006453 ◽

1981 ◽

Vol 24 (2) ◽

pp. 141-146 ◽

Cited By ~ 1

Author(s):

J. D. Mashburn

Keyword(s):

Fixed Point ◽

Upper Bound ◽

Partially Ordered Set ◽

Ordered Set ◽

Partially Ordered ◽

Fixed Point Properties ◽

Countable Chain ◽

Chain Complete

A partially ordered set, is ω-chain complete if, for every countable chain, or ω-chain, in P, the least upper bound of C, denoted by sup C, exists. Notice that C could be empty, so an ω-chain complete partially ordered set has a least element, denoted by 0.

Download Full-text