OPERATOR ACCRETIVE SINGLE-VALUED PADA RUANG BERNORMA

CHRISTINA KARTIKA S., Dr. Ch. Rini Indrati, M.Si

2015 | Tesis | S2 Matematika

Dalam tesis ini, dibahas operator accretive pada ruang bernorma X. Pertama, dipaparkan beberapa karakteristik operator accretive, salah satunya adalah operator accretive semi kontinu bawah merupakan operator single-valued pada interior domainnya. Selanjutnya, dibahas dua tipe operator terkait dengan operator accretive, yakni operator accretive-m dan operator disipatif. Dipaparkan juga solusi masalah Cauchy terkait operator disipatif. Keseluruhan materi yang dibahas digunakan untuk membuktikan untuk setiap z 2 X dan ?? > 0, terdapat x; u; v 2 X, dengan sifat z 2 G(u; v) + ??A(x), dengan A operator accretive dan G pemetaan yang memenuhi kondisi tertentu.

In this thesis, we discuss an accretive operator defined on a normed space X. First, we talk about some characteristics of the acccretive operator. One of them is lower semi-continuous accretive operator is single-valued operator on interior of its domain. Further, we discuss two types of operator related to accretive operator, accretive-m and dissipative operators. Solutions of Cauchy problem related to dissipative operator are discussed as well. All of our discussions are used to prove that for all z 2 X and ?? > 0, there are x; u; v 2 X such that z 2 G(u; v) + ??A(x), where A is an accretive operator and G is a mapping with certain conditions.

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