New Results on Parameterized Mercer type Inequalities: Analysis and Applications

Authors

  • Salih Tatar Department of Mathematics \& Computer Science, College of Science and General Studies, Alfaisal University, Riyadh, KSA
  • Arslan Munir School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026 People's Republic of, China
  • Muhammad Muawwaz Department of Mathematics, Riphah International University, Faisalabad Campus, Faisalabad, Pakistan. https://orcid.org/0009-0003-0811-3579
  • Ather Qayyum https://orcid.org/0000-0003-4149-5305

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i2.7646

Keywords:

Mercer-midpoint type inequalities, convex function, power-mean inequality, Mercer bullen type inequalities, Mercer Simspon's type inequalities, modified Bessel function, q-digamma function, quadrature schemes

Abstract

In this paper, we establish a Mercer-parameterized integral identity for differentiable functions. Using this identity, we derive a family of new parameterized Hermite--Hadamard-Mercer type inequalities for differentiable
convex functions. A key feature of the proposed results is their flexibility, which allows them to recover, as special cases, Mercer-type inequalities of trapezoidal, midpoint, Bullen-type, and Simpson-type. The validity and sharpness of the obtained inequalities are illustrated through mathematical examples and graphical representations. Moreover, the derived results extend several known inequalities in the existing literature. Finally, applications to the modified Bessel function, the q-digamma function, special means, and numerical quadrature schemes are presented.

Author Biographies

  • Salih Tatar, Department of Mathematics \& Computer Science, College of Science and General Studies, Alfaisal University, Riyadh, KSA

    Professor,

    Department of Mathematics \& Computer Science, College of
    Science and General Studies, Alfaisal University, Riyadh, KSA

  • Arslan Munir, School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026 People's Republic of, China

    PhD student

    School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026 People's Republic of, China

  • Ather Qayyum

    Post Doc Fellow,
    Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Malaysia 

References

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Published

2026-07-28

Issue

Vol. 19 No. 2: (April 2026)

Section

Mathematical Analysis

License

Copyright (c) 2026 Salih Tatar, Arslan Munir, Muhammad Muawwaz, Ather Qayyum

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How to Cite

New Results on Parameterized Mercer type Inequalities: Analysis and Applications. (2026). European Journal of Pure and Applied Mathematics, 19(2), 7646. https://doi.org/10.29020/nybg.ejpam.v19i2.7646