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All Journal Journal of the Indonesian Mathematical Society Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Hilbert Journal of Mathematical Analysis
Hakim, Denny Ivanal
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Chemistry Computer Science & IT Control & Systems Engineering Engineering Mathematics Physics

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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.
Revisiting Kantorovich Operators in Lebesgue Spaces Obie, Maximillian Ventura; Taebenu, Erick Angga; Gunadi, Reinhart; Hakim, Denny Ivanal
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 3 (NOVEMBER 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.3.1596.289-298

Abstract

According to the Weierstrass Approximation Theorem, any continuous function on the closed and bounded interval can be approximated by polynomials. A constructive proof of this theorem uses the so-called Bernstein polynomials. For the approximation of integrable functions, we may consider Kantorovich operators as certain modifications for Bernstein polynomials. In this paper, we investigate the behaviour of Kantorovich operators in Lebesgue spaces. We first give an alternative proof of the uniform boundedness of Kantorovich operators in Lebesgue spaces by using the Riesz-Thorin Interpolation Theorem. In addition, we examine the convergence of Kantorovich operators in the space of essentially bounded functions. We also give an example related to the rate of convergence of Kantorovich operators in a subspace of Lebesgue spaces.
A note on some Endpoint Estimates of Commutators of Fractional Integral Operators Wijaya, Verrel Rievaldo; Hakim, Denny Ivanal; Setya Budhi, Marcus Wono
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 3 (NOVEMBER 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.3.1599.322-327

Abstract

It is known that fractional integral operators are not bounded from Lebesgue integrable functions to Lebesgue space for some particular related exponent. Based on some recent results by Schikorra, Spector, and Van Schaftingen, we investigate commutators of fractional integral operators on Lebesgue integrable functions. We establish a weak type estimates for these commutators generated by essentially bounded functions. Under the same assumption, we also prove that the norm of these commutators are dominated by the norm of the Riesz transform.
Pointwise Multipliers of Orlicz-Morrey Spaces Ifronika, Ifronika; Hakim, Denny Ivanal; Budhi, Wono Setya
Journal of the Indonesian Mathematical Society Vol. 31 No. 4 (2025): DECEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i4.1965

Abstract

We investigate the space of pointwise multipliers of Orlicz-Morrey spaces. Using the H\"older inequality in Orlicz-Morrey spaces, we prove that the space of pointwise multipliers of Orlicz-Morrey spaces contains an Orlicz-Morrey space. We also prove a partial reverse inclusion of this result. In addition, we des\-cribe the space of pointwise multipliers of Orlicz-Morrey spaces by adding some growth conditions on Young functions. Our results can be viewed as an extension of the results on pointwise multipliers of Morrey spaces.
Co-Authors Ali, Amrizal Marwan Gunadi, Reinhart Ifronika, Ifronika Obie, Maximillian Ventura Setya Budhi, Marcus Wono Taebenu, Erick Angga Wijaya, Verrel Rievaldo Wono Setya Budhi Yudatama, Rizma