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Abstrak :
Fungsi konveks merupakan salah satu topik di analisis yang berkaitan erat dengan teori pertidaksamaan. Lebih lanjut, definisi fungsi konveks memiliki perluasan, yaitu fungsi s-konveks jenis pertama dan jenis kedua, untuk s elemen 0,1] tetap. Fungsi konveks berkaitan dengan pertidaksamaan Hermite-Hadamard-Fejer, yangmerupakan pertidaksamaan integral yang melibatkan fungsi konveks. Pengembangan lebih lanjut dari pertidaksamaan tersebut dilakukan dengan melibatkan fungsi s-konveks dan juga melalui konsep integral fraksional. Dalam skripsi ini dibahas bentuk-bentuk pertidaksamaan tipe Hermite-Hadamard-Fej ryang berlaku untuk fungsi s-konveks jenis kedua melalui integral fraksional Riemann-Liouville. Dari hasil tersebut diperoleh hubungan antara pertidaksamaan yang diperoleh dengan pertidaksamaan yang sama untuk fungsi konveks. ...... The convex function is one of the topics in mathematics that is closely related to the theory of inequality. Furthermore, the definition of convex function has an extension which is the first and second kind of s convex function, for fixed s elemen 0,1 . Convex function has a relation to the Hermite Hadamard Fejerinequality, which is an integral inequality involving a convex function. Further development of these inequalities involves the s convex function and also through the concept of fractional integral. In this study, we discuss theHermite Hadamard Fej r type inequality that applies to the second kind of s convex function via the Riemann Liouville fractional integral. From these results, the relationship between these inequalities with the same type of inequality for convex function, are obtained.

Abstrak :
Pertidaksamaan Hermite-Hadamard merupakan pertidaksamaan yang melibatkan integral yang berlaku pada fungsi konveks. Pertidaksamaan Hermite-Hadamard-Fej r merupakan perumuman dari pertidaksamaan Hermite-Hadamard dengan memberi bobot sebuah fungsi dengan syarat-syarat tertentu. Pengembangan dari pertidaksamaan Hermite-Hadamard-Fej r selanjutnya dapat berupa perumuman dari pertidaksamaan tersebut yang berlaku untuk integral fraksional. Pada penelitian ini dibahas mengenai bentuk-bentuk pertidaksamaan tipe Hermite-hadamard-Fej r yang berlaku untuk fungsi terturunkan dengan mutlak dari fungsi turunannya konveks melalui integral fraksional Riemann-Liouville. Penelitian ini merupakan studi literatur dari hasil yang sudah ada. Pertidaksamaan pada hasil yang diperoleh menunjukkan eksistensi dari pertidaksamaan tipe Hermite-Hadamard yang berlaku untuk jenis fungsi yang sama. ...... Hermite Hadamard inequality is an integral inequality holds for convex function. Hermite Hadamard Fej r inequality is the generalization of Hermite Hadamard inequality by giving a weight such a function with certain criterions. The next developed version of Hermite Hadamard Fej r inequality might be it's generalization holds for fractional integral. This study is about Hermite Hadamard Fej r type inequalities for differentiable mappings whose derivatives in absolute value are convex via fractional integral. This research is literature study by results that already exist. The obtained inequalities provided existence of Hermite Hadamard type inequalities for the same type functions.

Abstrak :
Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis.

Abstrak :
Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.

Abstrak :
No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Abstrak :
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. ...... 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.

Abstrak :
This book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems.