Sharper Jensen-Mercer operator inequalities with applications to quasi-arithmetic means

Slavica Ivelić Bradanović; Anita Matković; Jurica Perić; Slavica Ivelić Bradanović; Anita Matković; Jurica Perić

doi:10.3934/math.2026810

AIMS Mathematics

2026, Volume 11, Issue 7: 19952-17982. doi: 10.3934/math.2026810

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Sharper Jensen-Mercer operator inequalities with applications to quasi-arithmetic means

1.
Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia
2.
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Croatia
3.
Department of Mathematics, Faculty of Science, University of Split, Croatia

Received: 23 February 2026 Revised: 30 May 2026 Accepted: 11 June 2026 Published: 07 July 2026
MSC : 47A63, 47A64

Motivated by recent developments in the study of Jensen-Mercer type operator inequalities, this paper presents several new and more precise series of inequalities for self-adjoint operators on unital $ C^{\ast} $-algebras. Our approach is based on the concept of strong convexity, which allows the introduction of additional correction terms and the derivation of refined upper and lower bounds. The obtained results generalize and strengthen the classical Jensen-Mercer operator inequalities, both in the presence and absence of operator convexity. As an application, we establish new estimates for operator quasi-arithmetic means of the Mercer type and derive corresponding refinements for operator power means, including the arithmetic, geometric, and harmonic means.
- operator convex functions,
- convex functions,
- strongly convex functions,
- Jensen operator inequality,
- Jensen-Mercer operator inequality
Citation: Slavica Ivelić Bradanović, Anita Matković, Jurica Perić. Sharper Jensen-Mercer operator inequalities with applications to quasi-arithmetic means[J]. AIMS Mathematics, 2026, 11(7): 19952-17982. doi: 10.3934/math.2026810

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Abstract

Motivated by recent developments in the study of Jensen-Mercer type operator inequalities, this paper presents several new and more precise series of inequalities for self-adjoint operators on unital $ C^{\ast} $-algebras. Our approach is based on the concept of strong convexity, which allows the introduction of additional correction terms and the derivation of refined upper and lower bounds. The obtained results generalize and strengthen the classical Jensen-Mercer operator inequalities, both in the presence and absence of operator convexity. As an application, we establish new estimates for operator quasi-arithmetic means of the Mercer type and derive corresponding refinements for operator power means, including the arithmetic, geometric, and harmonic means.

References

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