Some inequalities and its applications

This thesis involves six chapters. The first chapter is summary of the literatüre and aim of the thesis. The second chapter consists of main definitions and theorems. In the third chapter numerical inequalities (Bernoulli inequality, Chebyshev inequality, Young inequality, Hölder inequality, Minkowski inequality, Hermite-Hadamard inequality, Jensen inequality, Schur inequality, Muirhead inequality) are examined. In the fourth chapter geometrical inequalities(mean inequality, isoperimetric inequalities, Brunn- Minkowski inequality)are included. In the fifth chapter function inequalities (Hilbert inequality, Hardy inequality, Hardy-Littlewood inequality, Riesz inequality, Wirtinger inequality, Bessel inequality) are explained. The sixth chapter includes conclusions and recommendations.