FUNGSI KONVEKS DAN PERTIDAKSAMAAN HERMITE-HADAMARD

    Nabil Mahatir, - (2021) FUNGSI KONVEKS DAN PERTIDAKSAMAAN HERMITE-HADAMARD. S1 thesis, Universitas Pendidikan Indonesia.

    Abstract

    Tujuan dari studi ini adalah mempelajari sifat-sifat Fungsi Konveks dan Pertidaksamaan Hermite-Hadamard. Sebagaimana diketahui bahwa sifat fungsi konveks telah digunakan untuk mengkonstruksi atau pengembangan pertidaksamaan Hermite-Hadamard. Pada studi ini dibahas tentang sifat-sifat fungsi konveks, serta hubungan fungsi konveks pada pertidaksamaan Hermite-Hadamard, yaitu fungsi konveks memenuhi pertidaksamaan Hermite-Hadamard. Untuk membuktikan kebalikannya, yaitu fungsi yang memenuhi pertidaksamaan Hermite-Hadamard adalah fungsi konveks, perlu penambahan syarat fungsi kontinu dan dengan menyatakan pertidaksamaan Hermite-Hadamard dalam bentuk pertidaksamaan yang melibatkan fungsi Steklov atau fungsi Iterasi Steklov. Pada penelitian ini dibahas pula ekstensi dari pertidaksamaan Hermite-Hadamard.

    Kata kunci: Fungsi Konveks, Pertidaksamaan Hermite-Hadamard, Fungsi Steklov, Fungsi Iterasi Steklov.

    Convex Function and Hermite-Hadamard Inequality

    ABSTRACT
    The aim of this study is to study the properties of the convex function and the Hermite-Hadamard Inequality. It is known that the characteristics of the convex function has been used to construct or develop the Hermite-Hadamard inequality. Furthermore, in this study, the properties of convex functions are discussed, as well as the relation between convex functions in the Hermite-Hadamard inequality, that is, the convex function satisfying the Hermite-Hadamard inequality. To prove the converse i.e. the function satisfying that the Hermite-Hadamard inequality is a convex function, it is necessary to add the condition for a continuous function and express the Hermite-Hadamard inequality in the form of an inequality involving the Steklov function or the Steklov Iteration function. This study also discusses the extension of the Hermite-Hadamard inequality.

    Keyword: Convex Function, Hermite-Hadamard Inequality, Steklov Function, Steklov Iteration Function.

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    Official URL: http://repository.upi.edu
    Item Type: Thesis (S1)
    Uncontrolled Keywords: Fungsi Konveks, Pertidaksamaan Hermite-Hadamard, Fungsi Steklov, Fungsi Iterasi Steklov.
    Subjects: L Education > L Education (General)
    Q Science > QA Mathematics
    Divisions: Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1 > Program Studi Matematika (non kependidikan)
    Depositing User: Nabil Mahatir
    Date Deposited: 06 Sep 2021 07:27
    Last Modified: 06 Sep 2021 07:27
    URI: http://repository.upi.edu/id/eprint/65695

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