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"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."

"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."

"Pertidaksamaan Hadamard adalah pertidaksamaan yang dibentuk oleh integral Riemann suatu fungsi konveks pada interval tertutup dengan integrasi numerik aturan titik tengah dan aturan trapesium. Hasil pengembangan dari pertidaksamaan Hadamard untuk fungsi terturunkan dan perkalian dua fungsi disebut pertidaksamaan tipe Hadamard. Studi literatur ini bertujuan untuk mempelajari beberapa pertidaksamaan tipe Hadamard berkaitan dengan fungsi-konveksi.

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Hadamard's inequality is formed by Riemann integral form of convex function and its approximation rules by using midpoint rule and trapezoidal rule. The extension of Hadamard?s inequality for differentiable function and products of two functions is called Hadamard type. This study of literature is studying about the Hadamard type inequalities based on s-convexity."

"The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p-laplace and porous medium type equations, both in the degenerate (p>2 or m>1) and in the singular range (1"

"A study of how complexity questions in computing interact with classical mathematics in the numerical analysis of issues in algorithm design. Algorithmic designers concerned with linear and nonlinear combinatorial optimization will find this volume especially useful. Two algorithms are studied in detail: the ellipsoid method and the simultaneous diophantine approximation method. Although both were developed to study, on a theoretical level, the feasibility of computing some specialized problems in polynomial time, they appear to have practical applications. The book first describes use of the simultaneous diophantine method to develop sophisticated rounding procedures. Then a model is described to compute upper and lower bounds on various measures of convex bodies. Use of the two algorithms is brought together by the author in a study of polyhedra with rational vertices. The book closes with some applications of the results to combinatorial optimization."

"This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. "

"Penelitian ini bertujuan untuk mengetahui pengaruh dari Upah Rata-Rata Per Jam Pekerja (URPJP), Rasio Gender Pada Angka Harapan Hidup (RAHH), Rasio Gender Pada Rata-Rata Lama Sekolah (RRLS), Rasio Gender Pada Tingkat Partisipasi Angkatan Kerja (RTPAK), Rasio Gender Pada Pengeluaran Per Kapita (RPP), dan Teknologi (T) terhadap Produktivitas Tenaga Kerja (Y) di Indonesia. Penarikan sampel dalam penelitian ini menggunakan teknik sampling jenuh di 34 provinsi Indonesia selama tahun 2018-2021 sehingga total sampel sebanyak 136 data yang diperoleh dari Badan Pusat Statistik (BPS). Penelitian ini menggunakan analisis data panel dengan mengganbungkan data time series dan data cross section. Hasil penelitian secara parsial menunjukkan bahwa variabel URPJP, RAHH, dan T berhubungan signifikan positif terhadap produktivitas tenaga kerja, sedangkan RRLS dan RPP berkorelasi positif namun tidak signifikan terhadap produktivitas tenaga kerja. Selain itu, RTPAK berhubungan signifikan negatif terhadap produktivitas tenaga kerja. Hasil penelitian secara simultan menunjukkan bahwa URPJP, RAHH, RRLS, RTPAK, RPP dan T berpengaruh terhadap produktivitas tenaga kerja.

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This study aims to determine the effect of Average Hourly Wages (URPJP), Gender Ratio on Life Expectancy Rate (RAHH), Gender Ratio on Average Years of Schooling (RRLS), Gender Ratio on Labor Force Participation Rate (RTPAK), Gender Ratio in Expenditures Per Capita (RPP), and Technology (T) to Labor Productivity (Y) in Indonesia. Sampling in this study used a saturated sampling technique in 34 Indonesian provinces during 2018-2021 so a total sample of 136 data was obtained from the Central Statistics Agency (BPS). This study uses panel data analysis by combining time series data and cross-section data. The results of the study partially show that the variables URPJP, RAHH, and T have a significant positive relationship to labor productivity, while RRLS and RPP have a positive correlation but are not significant to labor productivity. In addition, RTPAK has a significant negative relationship to labor productivity. The results of the study simultaneously show that URPJP, RAHH, RRLS, RTPAK, RPP, and T have an effect on labor productivity."

"For more than a century, the study of various types of inequalities has been the focus of great attention by many researchers, interested both in the theory and its applications. In particular, there exists a very rich literature related to the well known Cebysev, Gruss, Trapezoid, Ostrowski, Hadamard and Jensen type inequalities. The present monograph is an attempt to organize recent progress related to the above inequalities, which we hope will widen the scope of their applications. "