Prof. Dr. Mehmet Zeki Sarıkaya's research primarily focuses on analytical and applied aspects of mathematical inequalities, with a strong emphasis on integral inequalities, particularly those of Hermite-Hadamard, Simpson, Ostrowski, and trapezoidal type. His studies contribute significantly to convex analysis, including generalized convexity, quasi-convexity, and preinvexity, and their applications in inequality theory. He has a profound interest in special functions, such as Mittag-Leffler functions, hypergeometric functions, and generalized fractional operators, often using these in the framework of fractional calculus. Additionally, Prof. Sarıkaya explores generalized integral operators, Green functions, and Lidstone-type interpolations, with applications to approximation theory and mathematical modeling. His work is characterized by a rigorous analytical approach, often aiming to develop new inequalities or sharpen existing ones, which find applications in numerical integration, optimization, and theoretical physics.