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: firstname.lastname@example.org)
Full Text: PDF
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-quasisuperquadracityReferences:
- S. Abramovich, Hermite Hadamard, Fejer and Sherman type inequalities for generalizations of superquadratic and convex functions, J. Math. Inequal. 14 (2), 559–575, 2020.
- S. Abramovich, On compound superquadratic functions, Chapter 1 in Nonlinear Analysis, Differential Equations and Applications, Springer, 1-15, 2021.
- 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.
- S. Abramovich, G. Jameson and G. Sinnamon, Refining Jensen’s inequality, Bull. Math. Soc. Sci. Math. Roumanie 47, 3–14, 2004.
- M. Niezgoda, An extension of Levin-Steckin’s theorem to uniformly convex and superquadratic functions, Aequationes Math. 94, 303–321, 2020.
- 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.
- C. Zalinescu, On uniformly convex functions, J. Math. Anal. Appl. 95, 344–374, 1983.