Welcome to my Featured Publications page. This section highlights selected recent research contributions in mathematical inequalities, fractional calculus, generalized convexity, and related areas of mathematical analysis.
PUBLICATION 1 · 2026
Eze R. Nwaeze
International Journal of Theoretical Physics, Volume 65, Article 293 (2026).
Abstract: Motivated by a recent contribution published in the International Journal of Theoretical Physics, we develop a novel affine Jensen–Mercer inequality for coordinated convex functions that substantially broadens the scope of the existing theory. Building upon this unified framework, we establish new midpoint- and trapezoidal-type inequalities together with their Hölder- and power-mean refinements, thereby extending, generalizing, and complementing results in the aforementioned article. To investigate the influence of the affine structure, we conduct a comprehensive numerical study of the affine parameter c, illustrating its effect on the associated functionals and their corresponding theoretical upper bounds. Furthermore, by applying the proposed inequalities over partitioned rectangles, we derive composite affine midpoint- and trapezoidal-type estimates under coordinated convexity assumptions. Owing to the fundamental role of integral estimation in mathematical physics, these results may also be relevant to the estimation of integral quantities encountered in theoretical physics. Numerical computations and graphical illustrations corroborate the theoretical findings and illustrate the parameter-dependent behavior and flexibility of the proposed affine framework.
PUBLICATION 2 · 2026
Eze R. Nwaeze and Bosede O. Fagbemigun
Ukrainian Mathematical Journal, Volume 78, Article 46 (2026).
Abstract: The theory of multiplicative calculus has recently gained loads of attention. In this framework, the operations of addition and subtraction are systematically replaced with multiplication and division, respectively. The interest in this system is to obtain a multiplicative analog of the results obtained in the classical sense. Our aim is to contribute to the body of knowledge in this direction. Specifically, we establish some novel generalizations of the Hermite–Hadamard–Mercer-type inequalities involving new multiplicative tempered fractional integrals. A new lemma is also established. By using this lemma, Hölder’s inequality, and the power-mean inequality, we obtain more inequalities of the Trapezoid–Mercer type. Our results generalize many other results available from the literature. We present some numerical examples, utilizing the Wolfram Mathematica software for computations and graphing, to prove the validity of our results by comparing the outcomes for different values of the operating parameter λ ∈ [0, 1] with 0.1 as the step size. Finally, we obtain additional estimates by applying our results to special means, such as arithmetic, harmonic, logarithmic, and p-logarithmic means.
PUBLICATION 3 · 2026
Eze R. Nwaeze
Boundary Value Problems, Volume 2026, Article 2 (2026).
Abstract: A refined form of the Jensen–Mercer inequality has recently been introduced in the literature. Utilizing this improved inequality, we derive several new variants of the Hermite–Hadamard–Mercer type inequality, along with related estimates involving the beta function. These results serve to extend and generalize various existing inequalities. To demonstrate the validity of our findings, we provide numerical examples supported by both graphical and computational analyses. In addition, we explore applications of our results to specific means, including the arithmetic, harmonic, geometric, logarithmic, and p-logarithmic means. We hope that this work will stimulate further investigations in this area.