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Abdul Aziz

Departemen Matematika, FSM Universitas Diponegoro

Author-ID : 4393925

Decision Sciences, Operations Research & Management

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BEBERAPA KARAKTERISTIK BARU PADA FUNGSI TERDEKATI Abdul Aziz; Y.D. Sumanto; Solikhin Solikhin; Roberus Heri Utomo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 1 (2019)
Publisher : Diponegoro University

In this paper, discuss the relationship between approachable function with bounded variations, measurement, and absolute continuity. Futhermore, If f is approachable function of interval [a, b] then f is a bounded variation function and f is a measurable function of interval [a, b]. In relation with absolute continuity, if f is an absolute continuous of interval [a, b] then f is approachable function of [a, b].

RUANG BERNORMA LENGKAP ATAS OPERATOR LINEAR TERBATAS PADA RUANG FUNGSI TERINTEGRAL DUNFORD Solikhin Solikhin; YD Sumanto; Abdul Aziz; Susilo Hariyanto; R. Heri Soelistyo Utomo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 1 (2020)
Publisher : Diponegoro University

Abstract. We are discussed operator norms on space of Dunford integral function. We show that sets of all bounded linear operator from dual space of Banach space into space of Lebesgue integral function is Banach space. Abstrak. Artikel ini membahas norma operator atas operator linear terbatas pada ruang fungsi terintegral Dunford. Himpunan semua operator linear dari ruang dual atas ruang Banach ke ruang fungsi terintegral Lebesgue merupakan ruang bernorma yang lengkap terhadap norma operator yang diberikan.

SEMINORM PADA RUANG FUNGSI TERINTEGRAL DUNFORD Solikhin Solikhin; Y.D. Sumanto; Abdul Aziz
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 1 (2019)
Publisher : Diponegoro University

This article discussed the seminorm on Dunford integrable functional space. We show that the set of all Dunford integrable functions is linear space. The results were shown that $\left( D[a,b],\ \left\| \ \cdot \ \right\| \right)$ is a seminorm space with function defined by $\left\| f \right\|=\underset{\begin{smallmatrix} {{x}^{*}}\in {{X}^{*}} \\ \left\| {{x}^{*}} \right\|\le 1 \end{smallmatrix}}{\mathop{\sup }}\,\ \left\{ \underset{E\subset [a,b]}{\mathop{\sup }}\,\,\left| \left( L \right)\int\limits_{E}{{{x}^{*}}f} \right| \right\}$. Furthermore, $\left( D[a,b],\ d \right)$ is a pseudomatrix space with function defined by $d\left( f,g \right)=\left\| f-g \right\|=\underset{\begin{smallmatrix} {{x}^{*}}\in {{X}^{*}} \\ \left\| {{x}^{*}} \right\|\le 1 \end{smallmatrix}}{\mathop{\sup }}\,\ \left\{ \underset{E\subset [a,b]}{\mathop{\sup }}\,\,\left| \left( L \right)\int\limits_{E}{{{x}^{*}}\left( f-g \right)} \right| \right\}$.

RUANG BERNORMA PADA HIMPUNAN SEMUA FUNGSI TERDEKATI Abdul Aziz; Y.D. Sumanto; Solikhin Solikhin; Robertus Heri Soelistyo Utomo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 2 (2019)
Publisher : Diponegoro University

In this paper, we discuss that in the approachable functions set can be defined a complete norm. Furthermore, we obtained that all of approachable functions set is a Banach Space.

RELASI GREEN PADA GAMMA-SEMIGRUP YANG DIBANGKITKAN DARI SUATU SEMIGRUP YD Sumanto; Abdul Aziz; Solikhin Solikhin; R. Heri Soelistyo Utomo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 1 (2020)
Publisher : Diponegoro University

In the Gamma-semigroup generated from a semigroup, we can define some equivalence relations called the Green relation. Furthermore, we can examine the relationship between the Green relation on the Gamma-semigroup and the Green relation on it’s generating semigroup.

OPERATOR PADA RUANG FUNGSI TERINTEGRAL DUNFORD Solikhin Solikhin; Y.D. Sumanto; Susilo Hariyanto; Abdul Aziz
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 2 (2018)
Publisher : Diponegoro University

An integral Dunford and an operator on Dunford integrable functional space have discussed in this article. The results were shown that the Dunford integrable functional space was a linear function. For every Dunford integrable function on a closed interval, there is an operator that is linear bounded and weak compact operator, whereas its adjoin operator is also linear bounded and weak compact. An operator is weak compact if and only if its adjoin operator is weak compact. Furthermore, the norm of this operator was equal to the norm of its adjoin operator.

FUNGSI TERDEKATI DAN SIFAT-SIFATNYA Abdul Aziz; Susilo Hariyanto; Y.D. Sumanto; Solikhin Solikhin
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 2 (2018)
Publisher : Diponegoro University

In this paper, we have defined an approachable function using a simple function on a compact sets. Furthermore the simple properties of the function was examined and it was obtained that measurable function, continuous function, and bounded function are approachable function along the function space is a linier space.

NORMA OPERATOR PADA RUANG FUNGSI TERINTEGRAL DUNFORD Solikhin Solikhin; Susilo Hariyanto; Y.D. Sumanto; Abdul Aziz
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 2 (2019)
Publisher : Diponegoro University

We are discussed operator norms on spce of Dunford integral function. We show that for a function which Dunford integral, operator from dual space into space of Lebesgue integral is a bounded linear operator. Furthermore, sets of all bounded linear operator is a linear space and it is a normed space by norm certain. Finally, the distance function generated by the norm is metrix space.

Co-Authors R. Heri Soelistyo Utomo Robertus Heri Sulistyo Utomo Roberus Heri Utomo Solikhin Solikhin Susilo Hariyanto Y.D. Sumanto

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