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"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.

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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."

"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.

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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."

"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."

"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."

"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."

"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."

"Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications presents and analyzes numerous engineering models, illustrating the wide spectrum of potential applications of the new theoretical and algorithmical techniques emerging from the significant progress taking place in convex optimization. It is hoped that the information provided here will serve to promote the use of these techniques in engineering practice. The book develops a kind of "algorithmic calculus" of convex problems, which can be posed as conic quadratic and semidefinite programs. This calculus can be viewed as a "computationally tractable" version of the standard convex analysis."