My research focuses on mathematical inequalities and their applications, fractional calculus, generalized convexity, dynamical systems on time scales, and the geometry of zeros and growth properties of complex polynomials.
A central objective of my work is to develop new mathematical inequalities, establish refinements and generalizations of classical results, and investigate their connections with fractional integral operators and different classes of convex functions.
My research includes Hermite–Hadamard, Jensen–Mercer, Ostrowski, Simpson, and related inequalities, with particular emphasis on theoretical developments and applications in mathematical analysis.
I am also interested in collaborative research that connects mathematical inequalities with other areas of pure and applied mathematics.
This project investigates interior-point refinements of harmonic Hermite–Hadamard inequalities, including multi-level integral estimates, product inequalities, and applications to special means.
This research explores fractional integral identities and Hermite–Hadamard–Mercer-type inequalities for Banach-space-valued functions, with particular emphasis on differentiability, convexity, and Bochner integration.
This line of research concerns affine Jensen–Mercer inequalities, midpoint and trapezoidal estimates, and their applications to quadrature formulas and composite integral estimates.
This research investigates multiplicative calculus, generalized convexity, and fractional integral inequalities involving multiplicative Riemann–Liouville-type operators.
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