Some New Notions of Fractional Mercer-Hadamard-Type Inequalities over Generalized Convexity with Applications to Q-diagamma and Modified Bessel Functions

Authors

  • Jamshed Nasir Department of Mathematics, Virtual University of Pakistan, Lahore Campus, 54000, Pakistan
  • Muhammad Tariq Mathematics Research Center, Near East University, Near East Boulevard, PC: 99138, Nicosia /Mersin 10-Turkey
  • Waqar Afzal Center for Theoretical Physics, Khazar University, 41 Mehseti Str., Baku, AZ1096, Azerbaijan
  • Hijaz Ahmad Irfan Suat Gunsel Operational Research Institute, Near East University, Nicosia/TRNC, 99138 Mersin 10-Turkey; Department of Software Engineering, Karadeniz Technical University, 61080, Trabzon, Turkiye; Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea
  • Maggie Aphane Sefako Makgatho Health Sciences University, Garankuwa, Medusa, 0204, South Africa
  • Mustafa Bayram Department of Computer Engineering, Biruni University, Istanbul, Turkey
  • Mohamed Abbas EI-Naggar Department of General Subjects, University of Business and Technology, Jeddah 21361, Saudi Arabia; Chemical Engineering Department, Faculty of Engineering, Alexandria University, 21544, Egypt
  • Ilyas Khan Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India; Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, Jordan; Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia.

Keywords:

Mercer inequality, Hermite-Hadamard-Mercer inequalities, Jensen inequality

Abstract

This work develops Jensen–Mercer type inequalities for Æ-convex functions and leverages them to establish novel Mercer–Hadamard type inequalities pertaining to Riemann–Liouville fractional integral operators. Two auxiliary integral identities are artfully constructed to yield refined error bounds under the Æ-convexity of |T¢|q and |T¢¢|q for q ≥ 1. The resulting inequalities elegantly subsume and unify numerous classical results as special cases, recoverable through judicious choices of Æ and the fractional order ℓ. As compelling applications, sharp bounds for the Q` and the modified Bessel function of the first kind are crystallized.

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Published

2026-08-07

How to Cite

Jamshed Nasir, Muhammad Tariq, Waqar Afzal, Hijaz Ahmad, Maggie Aphane, Mustafa Bayram, … Ilyas Khan. (2026). Some New Notions of Fractional Mercer-Hadamard-Type Inequalities over Generalized Convexity with Applications to Q-diagamma and Modified Bessel Functions. Results in Nonlinear Analysis, 9(2), 105–130. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/860

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Vol. 9 No. 2 (2026): Volume 9 issue 2 - Current Issue

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