Soft Computing

, Volume 22, Issue 24, pp 8051–8058 | Cite as

Refinements of Hölder’s and Minkowski’s type inequalities for \(\sigma \)-\(\oplus \)-measures and pseudo-expectation

  • Hamzeh AgahiEmail author
  • Milad Yadollahzadeh


This paper gives some refinements of Hölder’s and Minkowski’s type inequalities and their relations to pseudo-expectation and g-semiring. These inequalities are studied for any \(\sigma \)-\(\oplus \)-measure with general kernels, including pseudo-expectation and pseudo-convolution integral. In special cases, our results improve and refine the previous results.


\(\sigma \)-\(\oplus \)-measure Hölder’s inequality Minkowski’s inequality Pseudo-expectation Probability measure 



The authors are very grateful to the anonymous reviewers for their suggestions which have led to an improved version of this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Basic ScienceBabol Noshirvani University of TechnologyBabolIran
  2. 2.Department of Mathematics, Faculty of Mathematical SciencesUniversity of MazandaranBabolsarIran

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