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Stability of approximate solution mappings for generalized Ky Fan inequality

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Abstract

This paper is concerned with the stability for a generalized Ky Fan inequality when it is perturbed by vector-valued bifunction sequence and set sequence. By continuous convergence of the bifunction sequence and Painlevé–Kuratowski convergence of the set sequence, we establish the Painlevé–Kuratowski convergence of the approximate solution mappings of a family of perturbed problems to the corresponding solution mapping of the original problem. Our main results are new and different from the ones in the literature.

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Acknowledgments

The authors would like to express their deep gratitude to the anonymous referees for their valuable comments and suggestions which helped to improve the paper.

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Authors and Affiliations

  1. College of Sciences, Chongqing Jiaotong University, Chongqing, 400074, China

    X. B. Li, Z. Lin & Q. L. Wang

Authors
  1. X. B. Li
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  2. Z. Lin
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  3. Q. L. Wang
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Corresponding author

Correspondence to X. B. Li.

Additional information

This research was partially supported by the National Natural Science Foundation of China (Grant Numbers 11201509 and 11271389), the Basic and Advanced Research Project of Chongqing (Grant Number cstc2014jcyjA00046), the Education Committee Project Research Foundation of Chongqing (Grant Number KJ1400304) and the Program for Core Young Teacher of the Municipal Higher Education of Chongqing ([2014]47).

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Li, X.B., Lin, Z. & Wang, Q.L. Stability of approximate solution mappings for generalized Ky Fan inequality. TOP 24, 196–205 (2016). https://doi.org/10.1007/s11750-015-0385-9

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