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All Journal Journal of the Indonesian Mathematical Society Jambura Journal of Mathematics Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Pattimura Proceeding : Conference of Science and Technology Hilbert Journal of Mathematical Analysis
Hakim, Denny Ivanal
Institut Teknologi Bandung
Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Energy Engineering Materials Science & Nanotechnology Mathematics Physics

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KETAKSAMAAN HERMITE-HADAMARD TERHADAP INTEGRAL RIEMANN-STIELTJES Denny Ivanal Hakim; Hendra Gunawan
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 4 No 1 (2012): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2012.4.1.2942

Abstract

The Hermite-Hadamard inequality is an inequality for convex functions that gives an estimate for the integral mean value of a convex function on a closed interval by its value at the middle of interval and the average of its values at the endpoints. The Hermite-Hadamard inequality can be generalized by using the Riemann-Stieltjes integral mean value. An application of the Hermite-Hadamard inequality with respect to Riemann-Stieltjes integral for estimating the power mean of positive real numbers by the aritmethic mean is given at the end of discussion.
OPERATOR KANTOROVICH PADA RUANG MORREY DIPERUMUM Mu’afa Purwa Arsana; Denny Ivanal Hakim
Pattimura Proceeding 2021: Prosiding KNM XX
Publisher : Pattimura University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1856.975 KB) | DOI: 10.30598/PattimuraSci.2021.KNMXX.107-114

Abstract

Pada makalah ini, kami mengkaji operator Kantorovich pada ruang Morrey diperumum. Kami membahas bukti keterbatasan operator Kantorvich di ruang Morrey diperumum pada interval [0,1], kunci untuk membuktikan keterbatasan operator Kantorvich pada ruang Morrey diperumum adalah dengan menggunakan estimasi operator Kantorovich dengan operator maksimal Hardy-Littlewood. Keterbatasan operator Kantorovich pada ruang Morrey (klasik) telah dibuktikan sebelumnya oleh Burenkov, dkk. Kami juga membahas kekonvergenan operator Kantorovich di ruang Morrey diperumum pada interval [0,1] dan memperoleh laju kekonvergenan operator Kantorvich
BUKTI ALTERNATIF INTERPOLASI KOMPLEKS RUANG LEBESGUE DENGAN EKSPONEN PEUBAH Dina Nur Amalina; Denny Ivanal Hakim
Pattimura Proceeding 2021: Prosiding KNM XX
Publisher : Pattimura University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1044.705 KB) | DOI: 10.30598/PattimuraSci.2021.KNMXX.61-66

Abstract

INTERPOLASI KOMPLEKS RUANG MORREY-ADAMS DAN OPERATOR MAKSIMAL FRAKSIONAL Daniel Salim; Moch Taufik Hakiki; Denny Ivanal Hakim
Pattimura Proceeding 2021: Prosiding KNM XX
Publisher : Pattimura University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1752.766 KB) | DOI: 10.30598/PattimuraSci.2021.KNMXX.83-90

Abstract

Makalah ini membahas interpolasi kompleks dari ruang Morrey-Adams. Khususnya, kami memberikan deskripsi interpolasi kompleks metode pertama dan metode kedua dari ruang ini. Bukti hasil ini menggunakan karakterisasi hasil kali Calder´on dari ruang Morrey Adams. Selain itu, kami juga membahas keterbatasan operator maksimal fraksional dari hasil kali Calder´on antara ruang Morrey- Adams dengan ruang Morrey ke ruang Morrey. Hasil pada makalah ini terkait dengan interpolasi ruang Morrey, interpolasi ruang B^u_w , dan aplikasi interpolasi kompleks pada keterbatasan operator maksimal fraksional di ruang Morrey.
KETERBATASAN OPERATOR TIPE VOLTERRA PADA RUANG MORREY ANALITIK L p,λ Moch Taufik Hakiki; Wono Setya Budhi; Denny Ivanal Hakim
Pattimura Proceeding 2021: Prosiding KNM XX
Publisher : Pattimura University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1033.049 KB) | DOI: 10.30598/PattimuraSci.2021.KNMXX.585-590

Abstract

Pada makalah ini,kami membahas syarat cukup dan perlu dari keterbatasan operator tipe Volterra pada ruang Morrey analitik Lp,λ = Lp,λ(D), untuk p > 1, dan 0 < λ < 1 pada cakram satuan D di bidang kompleks. Lebih lanjut, kami melakukan investigasi pada keterbatasan operator tipe Volterra dari ruang Morrey analitik Lp,λ(D) ke Lq,η(D), dengan p ≥ q > 1, 0 < λ < 1, dan η = 1− q p(1−λ). Hasil di kasus kedua ini memperluas hasil di kasus pertama, dan beberapa hasil yang telah diperoleh tentang keterbatasan operator tipe Volterra pada ruang fungsi analitik
Perluasan Masalah Isoperimetrik pada Bangun Ruang Andri Setiawan; Denny Ivanal Hakim; Oki Neswan
Jambura Journal of Mathematics Vol 5, No 2: August 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjom.v5i2.20534

Abstract

In this paper, several extensions of the isoperimetric problem in solid figures are explored, focusing on oblique and right prisms with rectangular, right-angled triangular, and regular hexagonal bases. The objective of this research is to find the prism with the largest volume while keeping the surface area constant. Through manipulations of algebra and simple trigonometry, evidence is obtained that a right prism provides a larger volume than an oblique prism if their surface areas are equal. By utilizing partial derivatives of a two-variable function and the Lagrange multiplier method, conditions for the side lengths are derived to obtain the prism with the maximum volume. The results show that a cube is the solution to the isoperimetric problem, meaning it has the largest volume among prisms with rectangular bases, while for the isoperimetric solution on prisms with right-angled triangular bases, the base of the prism must be an isosceles right-angled triangle. A regular hexagonal prism has a larger volume than prisms with rectangular and right-angled triangular bases if their surface areas are the same.
KETAKSAMAAN HERMITE-HADAMARD TERHADAP INTEGRAL RIEMANN-STIELTJES Denny Ivanal Hakim; Hendra Gunawan
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Vol 4 No 1 (2012): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2012.4.1.2942

Abstract

The Hermite-Hadamard inequality is an inequality for convex functions that gives an estimate for the integral mean value of a convex function on a closed interval by its value at the middle of interval and the average of its values at the endpoints. The Hermite-Hadamard inequality can be generalized by using the Riemann-Stieltjes integral mean value. An application of the Hermite-Hadamard inequality with respect to Riemann-Stieltjes integral for estimating the power mean of positive real numbers by the aritmethic mean is given at the end of discussion.
Eksplorasi Masalah Isoperimetrik pada Bangun Ruang Ali, Amrizal Marwan; Hakim, Denny Ivanal
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 12 Issue 1 June 2024
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v12i1.24918

Abstract

In two-dimensional figures, the isoperimetric problem is defined as finding two-dimensional figures that will produce the largest area among several two-dimensional figures with the same perimeter. In this research, the isoperimetric problem is extended to find the shape with the largest volume among the shapes that have the same surface area. The aim of this research is to solve isoperimetric problems in three-dimensional shapes obtained by comparing various shapes of three-dimensional shapes. The discussion in this research is limited to three-dimensional shapes in the form of prisms with regular n-sided bases, pyramids with regular n-sided bases, cylinders, cones, and spheres. This research method uses concepts from calculus, trigonometry and algebra to prove the isoperimetric theorem with a simple and elementary approach. The result of this research is that the order of the maximum volume of three-dimensional shapes if the surface area is the same from smallest to largest is a pyramid with an equilateral triangular base, a pyramid with a square base, a prism with an equilateral triangular base, a pyramid with a regular n-sided base (n≥5), cone, prism with square base, prism with regular n-sided base (n≥5), cylinder, and sphere.
Intermediate spaces on weak type discrete Morrey spaces Yudatama, Rizma; Hakim, Denny Ivanal
Hilbert Journal of Mathematical Analysis Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i2.33

Abstract

In this article we discuss inclusion between a discrete Morrey space and a weak discrete Morrey space as well as inclusion between two weak discrete Morrey spaces. By the inclusion properties of weak discrete Morrey spaces, we have intermediate spaces for the trivial case. Using the inclusion relation of discrete Morrey spaces and weak discrete Morrey spaces, we obtain that for the nontrivial case there is no weak discrete Morrey space between Banach pairs of weak discrete Morrey spaces except for the two weak discrete Morrey spaces itself.
Isoperimetric problems on n-sided prisms Ali, Amrizal Marwan; Hakim, Denny Ivanal
Hilbert Journal of Mathematical Analysis Vol. 3 No. 1 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i1.36

Abstract

In two-dimensional figure, the isoperimetric problem refers to finding two-dimensional figure that will produce the largest area among several shapes with equal perimeter. This research extends the isoperimetric problem to finding three-dimensional shapes with maximum volume among those having equal surface area. Our main goal is to solve the isoperimetric problem for prisms with regular n-sided base, prisms with irregular n-sided base and cylinder. In this research, the discussion is limited to prisms with regular and irregular bases. Our problem is equivalent with the problem of finding the smallest surface area of a given three-dimensional figure with the same volume. We will use a geometric approachin our proof. we will see the relationship between isoperimetric problems in two dimensional figures and isoperimetric problems in three-dimensional figure. We obtain the results of the isoperimetric problem from two prisms with regular n-sided bases and a prism with regular m-sided bases with n≤m, two prisms with regular n-sided bases and a prism with circular bases (cylinder), and two prisms with regular n-sided bases and a prism with irregular n-sided bases.
Co-Authors Abdul Karim Munir Aszari Akbar, Muhammad Imam Ali, Amrizal Marwan Amalina, Nur Dina Andri Setiawan Daniel Salim Gumilang, Aji Gunadi, Reinhart Hendra Gunawan Hendra Gunawan Ifronika, Ifronika Moch Taufik Hakiki Moch Taufik Hakiki Mu’afa Purwa Arsana Obie, Maximillian Ventura Oki Neswan Pratama, Aria Setya Budhi, Marcus Wono Taebenu, Erick Angga Wijaya, Verrel Rievaldo Wono Setya Budhi Wono Setya Budhi Yudatama, Rizma