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"Skripsi ini mempelajari beberapa variasi dari Ketaksamaan Mayorisasi diantaranya Ketaksamaan Mayorisasi Klasik Hardy-Littlewood-Pólya dan bentuk Integral Riemann dari ketaksamaan tersebut. Ketaksamaan klasik tersebut digeneralisasi dengan menggunakan konsep relatif konveks dan sebagai hasilnya diperoleh Generalisasi Ketaksamaan Mayorisasi Hardy- Littlewood-Pólya dan bentuk Integral Riemann dari ketaksamaan tersebut. Bukti dari versi generalisasi yang diberikan disini ditemukan oleh C.P Niculescu and F. Popovici. Beberapa contoh pengaplikasian dari ketaksamaan-ketaksamaan yang dihasilkan juga akan diberikan di skripsi ini seperti bukti dari ketaksamaan Jensen dan ketaksamaaan rataan pangkat.

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This skripsi studies some variance of Majorization Inequalities such as the Classical Hardy-Littlewood-Pólya Majorization Inequality together with its Riemann integral form. The classical inequality is generalized by using the concept of relative convexity and as a result we have The Generalization of Hardy-Littlewood-Pólya Majorization Inequality together with its Riemann integral form. The proof of the generalized version given here is due to C.P Niculescu and F. Popovici. Some examples of the application of the resulting inequalities will also be given in this skripsi such as the proof of Jensen inequality and power mean inequality."

"This skripsi studies some variance of Majorization Inequalities such as theClassical Hardy-Littlewood-Pólya Majorization Inequality together with itsRiemann integral form. The classical inequality is generalized by using theconcept of relative convexity and as a result we have The Generalization ofHardy-Littlewood-Pólya Majorization Inequality together with its Riemannintegral form. The proof of the generalized version given here is due to C.PNiculescu and F. Popovici. Some examples of the application of the resultinginequalities will also be given in this skripsi such as the proof of Jenseninequality and power mean inequality."