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On Monotone Maps: Semidifferentiable Case

  • Shashi Kant MishraEmail author
  • Sanjeev Kumar Singh
  • Avanish Shahi
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

In this paper, we define the concepts of monotonicity and generalized monotonicity for semidifferentiable maps. Further, we present the characterizations of convexity and generalized convexity in case of semidifferentiable functions. These results rely on general mean-value theorem for semidifferentiable functions (J Glob Optim 40:503–508, 2010).

Keywords

Generalized convexity Generalized monotonicity First-order conditions Semidifferentials 

Notes

Acknowledgements

The first author is financially supported by Department of Science and Technology, SERB, New Delhi, India, through grant no.: MTR/2018/000121. The second author is financially supported by CSIR-UGC JRF, New Delhi, India, through Reference no.: 1272/(CSIR-UGC NET DEC.2016). The third author is financially supported by UGC-BHU Research Fellowship, through sanction letter no: Ref.No./Math/Res/ Sept.2015/2015-16/918.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Shashi Kant Mishra
    • 1
    Email author
  • Sanjeev Kumar Singh
    • 1
  • Avanish Shahi
    • 1
  1. 1.Department of MathematicsInstitute of Science, Banaras Hindu UniversityVaranasiIndia

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