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A revised pre-order principle and set-valued Ekeland variational principles with generalized distances

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Abstract

In my former paper “A pre-order principle and set-valued Ekeland variational principle” (see [J. Math. Anal. Appl., 419, 904–937 (2014)]), we established a general pre-order principle. From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles (denoted by EVPs) in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy’s EVP in [On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381–396 (2011)], where the perturbation contains a weak τ-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle, but also can be applied to obtain the above Khanh and Quy’s EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances.

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Authors and Affiliations

  1. School of Mathematical Sciences, Soochow University, Suzhou, 215006, P. R. China

    Jing Hui Qiu

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  1. Jing Hui Qiu
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Correspondence to Jing Hui Qiu.

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Supported by National Natural Science Foundation of China (Grant Nos. 11471236 and 11561049)

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Qiu, J.H. A revised pre-order principle and set-valued Ekeland variational principles with generalized distances. Acta. Math. Sin.-English Ser. 33, 775–792 (2017). https://doi.org/10.1007/s10114-017-5062-5

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