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"The first chapter recalls some fundamental facts concerning bounded Selfadjoint operators on complex Hilbert spaces. The author also introduces and explores the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators that will play a central role throughout the book. The following chapter is devoted to the Ostrowski?s type inequalities, which provide sharp error estimates in approximating the value of a function by its integral mean and can be used to obtain a priory error bounds for different quadrature rules in approximating the Riemann integral by different Riemann sums. The author also presents recent results extending Ostrowski inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. The final chapter illustrates recent results obtained in extending trapezoidal type inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. Applications for mid-point inequalities and some elementary functions of operators as also provided."

"Pertidaksamaan Ostrowski adalah suatu pertidaksamaan integral untuk fungsi yang kontinu dan turunannya terbatas Pertidaksamaan tipe Ostrowski adalah hasil pengembangan dari pertidaksamaan Ostrowski yang dapat digunakan untuk mengetahui batas error dari suatu integrasi numerik Penelitian ini bertujuan untuk mempelajari beberapa pertidaksamaan tipe Ostrowski dan batas error yang diperoleh Fungsi yang digunakan adalah fungsi yang turunan pertamanya kontinu variasi terbatas kontinu mutlak dan fungsi Lipschitz Selain itu dalam penelitian ini juga dilakukan simulasi sederhana dari beberapa fungsi untuk melihat batas error dan kesesuaiannya dengan teori yang ada.

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Ostrowski`s inequality is an integral inequality for continuous functions and its derivative is bounded Ostrowski type inequalities is developed from Ostrowski`s inequality and it can be used to determine the error bound in numerical integration This research is studying about the Ostrowski type inequalities and its error bound especially for continuous function of bounded variation absolutely continous function and Lipschitz function Beside of that there is a simple simulation for some functions to get the error bound and check the compatibility with the theory."

"The main aim of this book is to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces. This text introduces the reader to the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators as well as the step functions of selfadjoint operators. The spectral decomposition for this class of operators, which play a central role in the rest of the book and its consequences are introduced. At the end of the chapter, some classical operator inequalities are presented as well."

"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."

"Dalam mengoperasikan mesin derek (crane), tentara yang menjadi operator duduk dalam keadaan statis dan perlu tingkat konsentrasi tinggi. Hal tersebut dapat beresiko menyebabkan terjadinya WSDM. Penelitian ini mencoba untuk mempelajari postur duduk yang ditimbulkan oleh desain kursi penumpang dalam lingkungan virtual dengan menggunakan software simulasi ergonomi, Jack 6.1. Penyesuaian dilakukan pada tinggi kursi, kemiringan sandaran kursi, tinggi tuas panel, dan pergeseran kursi untuk mendapatkan konfigurasi kursi yang ideal bagi tentara. Postur duduk yang terbentuk dari seluruh konfigurasi yang diujikan dinilai dengan menggunakan metode Posture Evaluation Index (PEI). Hasil penelitian berupa usulan kursi yang ergonomis bagi tentara Indonesia.

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While being transported using Armoured Personnel Carrier Vehicles, soldiers are seated in is static posture and giving a risk of WMSD. This study attempts to analyze the sitting posture caused by a passenger seat design in the virtual environment, using an ergonomics software simulation, Jack 6.1.

Adjustments have been made on the high of seat, back slope seat and distance of hand handle to obtain the ideal configuration for the soldiers. Sitting posture which is formed from all the tested configurations assessed using the method of Posture Evaluation Index (PEI). The purpose from this study is to design an ergonomic seat passenger models for Indonesian Soldiers."

"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. "

"This monograph is a presentation of a unified approach to a certain class of semimartingale inequalities, which can be regarded as probabilistic extensions of classical estimates for conjugate harmonic functions on the unit disc. The approach, which has its roots in the seminal works of Burkholder in the 80s, enables to deduce a given inequality for semimartingales from the existence of a certain special function with some convex-type properties. Remarkably, an appropriate application of the method leads to the sharp version of the estimate under investigation, which is particularly important for applications. These include the theory of quasiregular mappings (with deep implications to the geometric function theory), the boundedness of two-dimensional Hilbert transform and a more general class of Fourier multipliers, the theory of rank-one convex and quasiconvex functions, and more. The book is divided into a few separate parts. In the introductory chapter present motivation for the results and relate them to some classical problems in harmonic analysis. The next part contains a general description of the method, which is applied in subsequent chapters to the study of sharp estimates for discrete-time martingales, discrete-time sub- and supermartingales, continuous time processes, the square and maximal functions. Each chapter contains additional bibliographical notes included for reference.​ "

"This unabridged republication of the 1980 text, an established classic in the field, is a resource for many important topics in elliptic equations and systems and is the first modern treatment of free boundary problems. Variational inequalities (equilibrium or evolution problems typically with convex constraints) are carefully explained in An Introduction to Variational Inequalities and Their Applications. They are shown to be extremely useful across a wide variety of subjects, ranging from linear programming to free boundary problems in partial differential equations. Exciting new areas like finance and phase transformations along with more historical ones like contact problems have begun to rely on variational inequalities, making this book a necessity once again."