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A topological characterization of the existence of fixed points and applications
Author(s) -
Khanh Phan Quoc,
Quan Nguyen Hong
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300003
Subject(s) - mathematics , characterization (materials science) , convexity , fixed point , generalization , fixed point property , topology (electrical circuits) , fixed point theorem , pure mathematics , mathematical analysis , combinatorics , materials science , nanotechnology , financial economics , economics
We prove a topological two‐way characterization of the existence of fixed‐points, without using linear or convexity structures and provide applications in optimization‐related problems. Such a characterization is also demonstrated for a fixed‐component point, a slight generalization of a fixed point.