Equivalents of an approximate variational principle for vector-valued functions and applications

G. Y. Chen, X. X. Huang and G. M. Lee

Mathematical Methods of Operations Research, 1999, vol. 49, issue 1, 125-136

Abstract: In [1], we gave a unified variational principle for vector valued functions. In this paper, we give four equivalents of a corollary of this principle, generalizing the equivalence results of [3] to the vector case and improving the equivalence results of [5]. We also applied one of the equivalents to derive the vector form of the “Drop Theorem” ([3]). Applying the unified variational principle, we obtained a fixed point theorem for directional contractions as an application of our vector variational principle, generalizing a fixed point theorem for directional contractions in [9]. Copyright Springer-Verlag Berlin Heidelberg 1999

Keywords: Key words: Half distance; vector variational principle; fixed point of set-valued mappings; directional contraction (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:49:y:1999:i:1:p:125-136

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DOI: 10.1007/s001860050017

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