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Monotonicity and Circular Cone Monotonicity Associated with Circular Cones

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The circular cone \(\mathcal {L}_{\theta }\) is not self-dual under the standard inner product and includes second-order cone as a special case. In this paper, we focus on the monotonicity of \(f^{\mathcal {L}_{\theta }}\) and circular cone monotonicity of f. Their relationship is discussed as well. Our results show that the angle πœƒ plays a different role in these two concepts.

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Author information

Correspondence to Jein-Shan Chen.

Additional information

The author’s work is supported by National Natural Science Foundation of China (11101248, 11271233) and Shandong Province Natural Science Foundation (ZR2010AQ026, ZR2012AM016).

The author’s work is supported by Ministry of Science and Technology, Taiwan.

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Zhou, J., Chen, J. Monotonicity and Circular Cone Monotonicity Associated with Circular Cones. Set-Valued Var. Anal 25, 211–232 (2017). https://doi.org/10.1007/s11228-016-0374-7

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  • Circular cone
  • Monotonicity
  • Circular cone monotonicity

Mathematics Subject Classification (2010)

  • 26A27
  • 26B35
  • 49J52
  • 65K10