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All Journal Jurnal Pengajaran MIPA Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam EurekaMatika (Jurnal Online Matematika S1) Jurnal Analisa PRISMA BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Eurekamatika Kreano, Jurnal Matematika Kreatif Inovatif Diophantine Journal of Mathematics and Its Applications

Cece Kustiawan

Jurusan Pen.Matematika

Author-ID : 302718

Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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KEKONVERGENAN LEMAH PADA RUANG HILBERT Mubarak, Moch. Ramadhan; Sumiaty, Encum; Kustiawan, Cece
Jurnal EurekaMatika Vol 5, No 2 (2017): Jurnal EurekaMatika
Publisher : Mathematics Program Study, Universitas Pendidikan Indonesia (UPI)

ABSTRAK. Penelitian ini mengkaji mengenai kekonvergenan lemah padaruang Hilbert atas lapangan real. Kekonvergenan lemah termotivasi olehkekonvergenan kuat sehingga terdapat beberapa sifat dari kekonvergenankuat yang berlaku pada kekonvergenan lemah seperti ketunggalan limit,kelinearan limit, dan keterbatasan suatu barisan. Keterkaitan antarakonvergen kuat dan lemah mengakibatkan terdapat pendefinisian dan sifatsifatdaribarisanCauchylemahdanhimpunankompaksecarabarisandansecaralemah. Di akhir pembahasan dibicarakan mengenai keberlakuanTeorema Bolzano-Weierstrass pada ruang Hilbert.Kata kunci: Ruang Hilbert, konvergen kuat, konvergen lemah, himpunankompak secara barisan dan secara lemah, teorema Bolzano-Weiertrass.ABSTRACT. This study discusses the weak of convergence in Hilbertspace over the real field. The weak of convergence is motivated by a strongconvergence as a result that there are some properties of the strongconvergence which is applicable in the weak of convergence such asuniqueness of limit, linearity of limit, and boundedness of a sequence. Therelationship between strong and weak convergent implies that there are thedefinition and properties of weak Cauchy sequence and weakly compactset. In the end of the discussion discussed about the generalize of BolzanoWeierstrasstheoreminHilbertspace.Keywords: Hilbert Space, strong convergence, weak convergence, weaklycompact set, Bolzano-Weierstrass Theorem.

INTEGRAL PERRON DAN EKUIVALENSINYA DENGAN INTEGRAL DENJOY Nurandini, Riva Yasin; Sumiaty, Encum; Kustiawan, Cece
Jurnal EurekaMatika Vol 6, No 2 (2018): Jurnal EurekaMatika
Publisher : Mathematics Program Study, Universitas Pendidikan Indonesia (UPI)

ABSTRAK. Integral Perron adalah pengembangan dari integral Lebesgue, sehingga dengan menggunakan definisi integral Perron suatu fungsi yang tak terintegralkan Lebesgue dapat terintegralkan Perron. Sama halnya dengan integral Riemann dan integral Lebesgue, integral Perron juga memiliki sifat-sifat dasar integral diantaranya kelinearan, keterurutan, dan penambahan selang. Selain integral Perron, integral Denjoy juga merupakan pengembangan dari integral Lebesgue, hanya saja pendefinisian yang dilakukan oleh Denjoy berbeda dengan Perron. Oleh karena itu, pada penelitian ini akan dikaji hubungan antara integral Perron dan integral Denjoy, juga sifat-sifat yang dimiliki oleh integral Perron.Kata Kunci : Fungsi Mayor, Fungsi Minor, Turunan Atas, Turunan Bawah, ACG*, Integral Perron, Integral Denjoy.ABSTRACT.The Perron Integral is the development of the integral Lebesgue, by using Perron's integral definition an unintegrated function of Lebesgue can be integrated Perron. Similar to the Riemann integral and the Lebesgue integral, the Perron integral also has the integral basic properties such as linearity, obedience, and the addition of a line. In addition to the integral Perron, the integral Denjoy is also the development of the integral Lebesgue, but the definition of Denjoy is different from Perron. Therefore, in this study will examine the relationship between the Perron integral and Denjoy integral, also the properties possessed by the Perron integral.Keyword : Major Function, Minor Function, Upper Derivative, Lower Derivative, ACG*, Perron Integral, Denjoy Integral.

Co-Authors Aan Hasanah Dadang Juandi Dasep, Dasep Encum Sumiaty, Encum Endang Mulyana Entit puspita Fitria, Nida Fitrian, Ressa Khusnul Novianingsih Marsyanda, Meifa Putri Masta, Al Azhary Mubarak, Moch. Ramadhan Mulvi Ludiana Nurandini, Riva Yasin Siti Fatimah Suhendra Suhendra Sumanang Muhtar Gojali Yudi Aditya

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