Articles
<![CDATA[Teorema titik tetap di ruang Banach ]]>
<![CDATA[Husnia, Amanatul]]>;
<![CDATA[Rahman, Hairur]]>
<![CDATA[ CAUCHY Vol 3, No 2 (2014): CAUCHY ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/ca.v3i2.2582
<![CDATA[Ruang Banach merupakan suatu konsep penting dalam analisis fungsional. Pada tahun 1992, seorang ahli matematika berasal dari Polandia membuktikan teorema yang menyatakan ketunggalan titik tetap. Teorema tersebut disebut juga dengan teorema titik tetap Banach. Teorema titik tetap Banach (teorema kontraksi) merupakan teorema ketunggalan dari suatu titik tetap pada suatu pemetaan yang disebut kontraksi dari ruang metrik lengkap ke dalam dirinya sendiri. Pengertian ruang Banach sendiri adalah ruang norm yang lengkap, dikatakan lengkap jika barisan Cauchy tersebut konvergen. Penelitian ini bertujuan untuk mengetahui pembuktian titik tetap di ruang Banach dengan kondisi yang diberikan yaitu pada pemetaan Kannan dan pemetaan Fisher. Berdasarkan hasil pembahasan, diperoleh bahwa pemetaan Kannan dan pemetaan Fisher mempunyai titik tetap yang tunggal ð‘‡(ð‘¥)=ð‘¥ dan pemetaan tersebut merupakan pemetaan titik tetap terhadap dirinya sendiri di ruang metrik lengkap]]>
<![CDATA[Linieritas Integral Henstock-Pettis pada Ruang Euclide Rn ]]>
<![CDATA[Rahman, Hairur]]>
<![CDATA[ CAUCHY Vol 1, No 2 (2010): CAUCHY ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/ca.v1i2.1705
<![CDATA[In this paper we study Henstock-Pettis integral on the Euclidean space â„œn. We discuss some properties Linear integrable]]>
<![CDATA[Kestabilan Persamaan Fungsional Jensen ]]>
<![CDATA[Nisa', Hilwin]]>;
<![CDATA[Rahman, Hairur]]>;
<![CDATA[Sujarwo, Imam]]>
<![CDATA[ CAUCHY Vol 3, No 4 (2015): CAUCHY ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/ca.v3i4.2922
<![CDATA[Persamaan fungsional Jensen merupakan variasi dari persamaan fungsional Cauchy additive yang paling sederhana dan paling bagus. Persamaan fungsional Jensen dapat diaplikasikan sebagai model dari suatu proses fisik ketika persamaan fungsional Jensen tersebut stabil. Oleh karena itu, dengan diketahuinya kestabilan dari persamaan fungsional tersebut, dapat menambah referensi para peneliti lain yang akan mengaplikasikan persamaan fungsional Jensen. Pada artikel ini akan ditunjukkan kestabilan persamaan fungsional Jensen. Untuk mengetahui kestabilannya digunakan teorema kestabilan Hyers-Ulam-Rassias. Berdasarkan hasil analisis, telah dibuktikan bahwa persamaan fungsional Jensen telah memenuhi teorema kestabilan Hyers-Ulam-Rassias, sehingga dapat dikatakan bahwa persamaan fungsional Jensen tersebut stabil.]]>
<![CDATA[PEMBELAJARAN KONTRUKTIFISTIK DENGAN PENDEKATAN CTL PADA TEORI BELAJAR BERMAIN DIENES ]]>
<![CDATA[Rahman, Hairur]]>
<![CDATA[ Madrasah: Jurnal Pendidikan dan Pembelajaran Dasar Vol 1, No 2 (2009): Madrasah: Jurnal Pendidikan dan Pembelajaran Dasar ]]>
Publisher : <![CDATA[Fakultas Ilmu Tarbiyah dan Keguruan Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/jt.v1i2.1849
<![CDATA[In order to improve the students’ mastering at elementary schools, it is important to note that the teaching strategies should not be only focused on “how to teachâ€, however the teaching should be also focused on “how to stimulate†and “how to learnâ€. In this context, the contextual teaching and learning approach (CTL) is considered as the new approach, particularly for math subject, which has been applied in Indonesia. For this purpose, this article offers the concept teaching model by Dienes theory using CTL approach.Kata Kunci: CTL, Konstruktivisme, Teori Belajar Bermain Dienes.  ]]>
<![CDATA[Inclusion Properties of The Homogeneous Herz-Morrey ]]>
<![CDATA[Rahman, Hairur]]>
<![CDATA[ CAUCHY Vol 6, No 3 (2020): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/ca.v6i3.10114
<![CDATA[In this paper, we have discussed about the inclusion properties of the homogeneous Herz-Morrey spaces and the homogeneous weak homogeneous spaces. We also studied the inclusion relation between those spaces.]]>
<![CDATA[Inclusion Properties of The Homogeneous Herz-Morrey Spaces With Variable Exponent ]]>
<![CDATA[Rahman, Hairur]]>
<![CDATA[ CAUCHY Vol 7, No 1 (2021): CAUCHY: Jurnal Matematika Murni dan Aplikasi ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/ca.v7i1.12141
<![CDATA[In this paper, we have discussed about the inclusion properties of the homogeneous Herz-Morrey spaces with variable exponent and the weak homogeneous spaces with variable exponent. We also studied the inclusion relation between those spaces.]]>
<![CDATA[Syarat Cukup Ketaksamaan Holder di Ruang Lebesgue dengan Variabel Eksponen ]]>
<![CDATA[Ba'is, Mohamad Abdul]]>;
<![CDATA[Rahman, Hairur]]>;
<![CDATA[Herawati, Erna]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 2, No 1 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v2i1.14619
<![CDATA[Hӧlder inequality is a basic inequality in functional analysis. The inequality used for proofing other inequalities. In this research, the development of the application of the Hӧlder inequality in the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent. The integral Hӧlder inequality is used because the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent is a function space.This research shows the sufficient condition of Hӧlder inequality in Lebesgue spaces with variable exponent and the Morrey spaces with variable exponent according to the norm of the function and its characteristics.]]>
<![CDATA[Model Epidemi Suspected Exposed Infected Recovered (SEIR) Pada Penyebaran COVID-19 Orde-Fraksional ]]>
<![CDATA[Nisa, Khoirotun]]>;
<![CDATA[Rahman, Hairur]]>;
<![CDATA[Kusumastuti, Ari]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 3 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i3.14440
<![CDATA[This article discusses the solution to the fractional order SEIR equation with the help of the Homotopy Perturbation Method (HPM). This mathematical model is the SEIR model of the spread of COVID-19 cases in Indonesia. In general, the nonlinear Ordinary Differential Equation System (ODES) solution is quite difficult to solve analytically, so this research will transform the nonlinear ODES into a Fractional Differential Equation System (FDES). The method used in completing this research is the HPM method. The solution for the fractional order by the HPM method is obtained by the following steps: 1). Multiply each SEIR equation against the embedding parameter and equate each coefficient in the assumed infinite series to find the solution, 2). Simulate numerical solutions and perform graph interpretation. The numerical simulation shows that the susceptible human population, the infected human population without symptoms, the recovered human population has increased, in contrast to the infected human population with decreased symptoms. The HPM method in its numerical solution shows a fairly small comparison to the nonlinear ODES solution.]]>
<![CDATA[Ruang l^p pada Norm-2 Lengkap ]]>
<![CDATA[Utami, Sri]]>;
<![CDATA[Rahman, Hairur]]>;
<![CDATA[Ismiarti, Dewi]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i4.14464
<![CDATA[The space l^p with 1≤p∞ is the set of real numbers that satisfy _(n=1)^∞▒〖|x_n |^p∞〗.The function in the vector space X which has real value which fulfills the norm-2 properties is denoted by ,⋅‖ and the pair (X,‖⋅,⋅‖) is called the norm-2 space.A norm-2 space is said to be complete or called a Banach-2 space if every Cauchy sequence in the space converges to an element in that space.This research was conducted to prove the l^p space in the complete norm-2.The first step to prove the completeness is to prove that the norm contained in l^p with 1≤p∞ satisfies the properties of norm-2.Next, prove that the norm derived from norm-2 is equivalent to the norm in l^p.Next shows that every Cauchy sequence in space l^p converges to an element in space l^p.Based on this proof, it is found that (l^p,‖⋅,⋅‖) is a complete norm-2 space.]]>
<![CDATA[Operator Integral Fraksional yang diperumum pada Ruang Morrey yang diperumum ]]>
<![CDATA[Putri, Safira Nur Aulia]]>;
<![CDATA[Rahman, Hairur]]>;
<![CDATA[Nasichuddin, Achmad]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 3, No 3 (2024): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v3i3.16973
<![CDATA[The fractional integral operator or Riesz operator is a finite operator of the Lebesgue space. This fractional integral operator maps any real-valued function into the integral form of the fractional integral function. Morrey space is a collection of general form member functions of Lebesgue space. In this study, we will discuss the generalized fractional integral operator on a generalized Morrey space. The proof will be done using partitioned. It can be concluded that the generalized fractional integral operator on Morrey space generalized to Theorem A and Theorems B .]]>
