The article explores different types of inequalities using the Mond-Pecaric method. It discusses Jensen's inequality, Kantorovich inequality, and converses of Jensen's inequality. The researchers apply the Mond-Pecaric method to find bounds and investigate sharp inequalities. They also study inequalities for power operator means and the Hadamard product of operators. Additionally, the article examines the preservation of operator order and chaotic order in various functions.