Article ID: MTJPAM-D-21-00063

Title: Uniform Convexity, N-quasisuperquadracity, N-quasiconvexity and Extensions of the Euler-Lagrange Identity

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00063; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 139-151

Document Type: Research Paper

Author(s): Shoshana Abramovich a

aDepertment of Mathematics, University of Haifa, Haifa, Israel

Received: 8 November 2021, Accepted: 31 March 2022, Published: 13 May 2022.

Corresponding Author: Shoshana Abramovich (Email address:

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Using convexity, ψ-uniformly convexity, N-quasiconvexity and N-quasisuperquadracity we extend and refine inequalities related to the Euler-Lagrange identity.

Keywords: Euler-Lagrange identity, Convexity, ψ-uniformly convexity, N-quasiconvexity, Superquadracity, N-quasisuperquadracity

  1. S. Abramovich, Hermite Hadamard, Fejer and Sherman type inequalities for generalizations of superquadratic and convex functions, J. Math. Inequal. 14 (2), 559–575, 2020.
  2. S. Abramovich, On compound superquadratic functions, Chapter 1 in Nonlinear Analysis, Differential Equations and Applications, Springer, 1-15, 2021.
  3. S. Abramovich, S. Ivelić and J. Pečarić, Extension of the Euler-Lagrange identity by superquadratic power functions, Int. J. Pure Appl. Math. 74 (2), 209–220, 2012.
  4. S. Abramovich, G. Jameson and G. Sinnamon, Refining Jensen’s inequality, Bull. Math. Soc. Sci. Math. Roumanie 47, 3–14, 2004.
  5. M. Niezgoda, An extension of Levin-Steckin’s theorem to uniformly convex and superquadratic functions, Aequationes Math. 94, 303–321, 2020.
  6. S.-E. Takahasi, J. M. Rassias, S. Saitoh and Y. Takahashi, Refined generalization of the triangle inequality on Banach spaces, Math. Inequal. Appl. 13 (4), 733–741, 2010.
  7. C. Zalinescu, On uniformly convex functions, J. Math. Anal. Appl. 95, 344–374, 1983.