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].
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Manuscript received: October 1997/final version received: July 1998
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Chen, G., Huang, X. & Lee, G. Equivalents of an approximate variational principle for vector-valued functions and applications. Mathematical Methods of OR 49, 125–136 (1999). https://doi.org/10.1007/s001860050017
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DOI: https://doi.org/10.1007/s001860050017