Functional inequalities in matrix Banach spaces

  • Sundas Nawaz
  • Afshan Batool
  • Muhammad Arshad Zia
  • Choonkil ParkEmail author


Using fixed point method, we prove the Hyers–Ulam stability of the following functional inequalities \( \Vert f(x)+f(y)+f(z)\Vert \le \Vert f(x+y+z)\Vert \) and \( \Vert f(x)+f(y)+2f(z)\Vert \le \Vert 2f(\frac{x+y}{2}+z)\Vert \) in matrix Banach spaces.


Functional inequality matrix Banach space additive mapping fixed point Hyers–Ulam stability 

Mathematics Subject Classification

39B62 39B42 47H10 65F35 



C. Park was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2017R1D1A1B04032937).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sundas Nawaz
    • 1
  • Afshan Batool
    • 2
  • Muhammad Arshad Zia
    • 1
  • Choonkil Park
    • 3
    Email author
  1. 1.Department of MathematicsInternational Islamic UniversityIslamabadIslamic Republic of Pakistan
  2. 2.Department of Mathematical SciencesFatima Jinnah Women UniversityRawalpindiIslamic Republic of Pakistan
  3. 3.Research Institute for Natural SciencesHanyang UniversitySeoulSouth Korea

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