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"Set-valued function (fungsi bernilai himpunan) adalah salah satu jenis fungsi yang banyak diteliti oleh para ahli dewasa ini. Salah satu sifat pemetaan yang menjamin titik tetap pada set-valued function yang sudah dikenal adalah sifat kontraktif. Pada tesis ini, dikaji eksistensi titik tetap set-valued function dengan sifat pemetaan C-kontraktif menggunakan konsep metrik Hausorff. Dari hasil penelitian didapat bahwa eksistensi titik tetap set-valued function dengan sifat pemetaan C-kontraktif masih dapat dipertahankan.

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Set-valued function is a kind of function that has an improvement in research. One kind of a famous mapping that guarantee a fixed point in a setvalued function is contractive mapping. In this thesis an analyse of fixed point of set-valued function with C-contractive mapping using Hausdorff metric is done. From the research, the existence of fixed point in a set-valued function with Contractive mapping still be remained."

"This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. "

"Salah satu perumuman dari ruang metrik adalah ruang metrik parsial. Ruang metrik parsial merupakan (X, p) dengan X merupakan himpunan tak kosong dan p : X × X → R merupakan metrik parsial pada X, yaitu pemetaan bernilai R pada X×X yang memenuhi beberapa aksioma. Nilai metrik parsial tersebut dapat diperumum menjadi aljabar-C* unital A, sehingga dibentuk ruang metrik parsial bernilai aljabar-C* (X, A, p) dengan X merupakan himpunan tak kosong dan p : X × X → A merupakan metrik parsial bernilai aljabar-C* pada X, yaitu pemetaan bernilai A pada X × X yang memenuhi beberapa aksioma. Titik tetap dari pemetaan pada suatu himpunan, khususnya ruang metrik, adalah titik yang dipetakan ke dirinya sendiri. Teorema titik tetap merupakan teorema mengenai eksistensi dan ketunggalan titik tetap dari pemetaan pada ruang metrik. Pada skripsi ini, ditentukan dan dibuktikan hubungan ruang metrik parsial bernilai aljabar-C* dengan ruang metrik bernilai aljabar-C*. Selain itu, dibuktikan teorema titik tetap dari pemetaan kontraktif bernilai aljabar-C* pada ruang metrik parsial bernilai aljabar-C*.

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One of the extension of metric spaces is partial metric spaces. A partial metric space is a pair (X, p) where X is a nonempty set and p : X × X → R is a partial metric on X, which is a real valued mapping on X × X that satisfy some axioms. The value of partial metrics can be generalized to a unital C*-algebra A, so that we can form a C*-algebra valued partial metric space (X, A, p) where X is a nonempty set and p : X × X → A is a C*-algebra valued partial metric on X, which is a A-valued mapping on X × X that satisfy some axioms. A fixed point of a mapping on a set, particularly metric space, is a point that is mapped to itself. Fixed point theorems are theorems regarding existence and uniqueness of a fixed point of a mapping on metric spaces. In this research, we establish and prove the relations between C*-algebra valued partial metric spaces and C*-algebra valued metric spaces. Furthermore, we prove a fixed point theorem of a C*-algebra valued contractive mapping on C*-algebra valued partial metric spaces."

"It provides readers with a complete guide to problems in these fields as well as a detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization is not just for students, however; it is a comprehensive guide for anyone who wants to approach the field of variational analysis in a systematic way, starting from the most classical examples and working up to a research level. This book also contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references."

"Titik x dikatakan titik tetap dari sembarang pemetaan T jika dan hanya jika T x = x. Berbagai hasil mengenai teorema titik tetap telah dibuktikan pada ruang metrik. Seiring berkembangnya bidang analisis matematis, semakin banyak matematikawan yang berhasil membuktikan teorema titik tetap di berbagai ruang dan pemetaan. Namun, tidak banyak hasil mengenai teorema titik tetap yang telah dibuktikan pada ruang dislocated quasi b-metric. Ruang dislocated quasi b-metric adalah salah satu bentuk perluasan dari ruang metrik dimana jarak antara dua buah titik yang sama tidak harus bernilai nol yaitu d(x, x) =/= 0 serta sifat simetri yaitu d(x, y) = d(y, x) tidak berlaku di ruang ini. Pada skripsi ini, akan dibuktikan kembali teorema-teorema mengenai ketunggalan titik tetap pada ruang dislocated quasi b-metric untuk sembarang pemetaan. Pada Skripsi ini juga akan dibahas mengenai teorema titik tetap untuk pemetaan tipe F-kontraktif pada ruang yang sama.

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A point x is said to be a fixed point of a mapping T on a nonempty set X if and only if T x = x. Many results regarding the fixed point theorem have been proved on metric spaces. As the field of mathematical analysis develops, more and more mathematicians have succeeded in proving fixed point theorems in various spaces and mappings. However, not many results regarding the fixed point theorem have been proved on dislocated quasi b-metric spaces. Dislocated quasi b-metric space is one of the extensions of metric space where the distance between two equal points does not have to be zero i.e. d(x, x) =/= 0 and the symmetry property i.e. d(x, y) = d(y, x) does not apply in this space. In this thesis, we will prove the theorems on the uniqueness of fixed points on dislocated quasi b-metric spaces for any mapping. This thesis also discusses the fixed point theorem for F-contractive type mappings in the same space."

"A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces."

"[ABSTRAKPM2,5 dapat masuk ke alveoli dan menjadi pemicu terjadinya inflamasi sehingga menyebabkan penurunan fungsi paru. Tujuan dari penelitian ini adalah untuk menganalisis secara spasial hubungan antara konsentrasi PM2,5 udara dalam rumah dengan penurunan fungsi paru pada ibu rumah tangga sekitar industri Desa Sukadanau, Kecamatan Cikarang Barat, Kabupaten Bekasi tahun 2015. Desain penelitian cross sectional modifikasi geographical epidemiology pada 125 ibu rumah tangga berusia 20-45 tahun yang akan diperiksa fungsi parunyamenggunakan spirometri serta 125 sampel PM2,5 udara dalam rumah. Hasil penelitian menunjukkan bahwa terdapat 58,4% ibu rumah tangga yang mengalami penurunan fungsi paru. Hasil analisis multivariat dapat disimpulkan bahwa ibu rumah tangga berusia 20-45 tahun yang tinggal di rumah dengan konsentrasi PM2,5 tidak memenuhi syarat berisiko 2,4 kali lebih besar mengalami penurunan fungsi paru dibandingkan ibu rumah tangga yang tinggal di dalam rumah dengankonsentrasi PM2,5 memenuhi syarat setelah dikontrol variabel ventilasi dan pajanan asap rokok. Analisis spasial menunjukkan RW 5 dan RW 8 Desa Sukadanau, Kecamatan Cikarang Barat merupakan wilayah RW dengan zona prioritas untuk dilakukan intervensi kesehatan.

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ABSTRACTFine particles more dangerous because they penetrate more deeply into the lung and may reach the alveolar region and reduce lung function. The aim of this study was to analys spatially association between indoor fine particles and lung function levels among housewife around steel industry. A cross sectional design study combine with geographical epidemiology of 125 houses that the unit analysis were 125 housewives from 20 to 45 years. The results showed that there were 58,4% housewives had decline lung function. Multivariate analysis concluded that housewives aged 20-45 years with indoor fine particles (PM2,5) inadequate 2.4 times risk higher to reduced lung function than adequate indoor fine particles after controlled by ventilation and tobacco smoke exposure. Spatial analysis concluded that RW 5 and RW 8 Sukadanau, West Cikarang were in priority zone with very high risk area.;Fine particles more dangerous because they penetrate more deeply into the lungand may reach the alveolar region and reduce lung function. The aim of this studywas to analys spatially association between indoor fine particles and lung functionlevels among housewife around steel industry. A cross sectional design studycombine with geographical epidemiology of 125 houses that the unit analysiswere 125 housewives from 20 to 45 years. The results showed that there were58,4% housewives had decline lung function. Multivariate analysis concluded thathousewives aged 20-45 years with indoor fine particles (PM2,5) inadequate 2.4times risk higher to reduced lung function than adequate indoor fine particles aftercontrolled by ventilation and tobacco smoke exposure. Spatial analysis concludedthat RW 5 and RW 8 Sukadanau, West Cikarang were in priority zone with veryhigh risk area.;Fine particles more dangerous because they penetrate more deeply into the lungand may reach the alveolar region and reduce lung function. The aim of this studywas to analys spatially association between indoor fine particles and lung functionlevels among housewife around steel industry. A cross sectional design studycombine with geographical epidemiology of 125 houses that the unit analysiswere 125 housewives from 20 to 45 years. The results showed that there were58,4% housewives had decline lung function. Multivariate analysis concluded thathousewives aged 20-45 years with indoor fine particles (PM2,5) inadequate 2.4times risk higher to reduced lung function than adequate indoor fine particles aftercontrolled by ventilation and tobacco smoke exposure. Spatial analysis concludedthat RW 5 and RW 8 Sukadanau, West Cikarang were in priority zone with veryhigh risk area.;Fine particles more dangerous because they penetrate more deeply into the lungand may reach the alveolar region and reduce lung function. The aim of this studywas to analys spatially association between indoor fine particles and lung functionlevels among housewife around steel industry. A cross sectional design studycombine with geographical epidemiology of 125 houses that the unit analysiswere 125 housewives from 20 to 45 years. The results showed that there were58,4% housewives had decline lung function. Multivariate analysis concluded thathousewives aged 20-45 years with indoor fine particles (PM2,5) inadequate 2.4times risk higher to reduced lung function than adequate indoor fine particles aftercontrolled by ventilation and tobacco smoke exposure. Spatial analysis concludedthat RW 5 and RW 8 Sukadanau, West Cikarang were in priority zone with veryhigh risk area., Fine particles more dangerous because they penetrate more deeply into the lungand may reach the alveolar region and reduce lung function. The aim of this studywas to analys spatially association between indoor fine particles and lung functionlevels among housewife around steel industry. A cross sectional design studycombine with geographical epidemiology of 125 houses that the unit analysiswere 125 housewives from 20 to 45 years. The results showed that there were58,4% housewives had decline lung function. Multivariate analysis concluded thathousewives aged 20-45 years with indoor fine particles (PM2,5) inadequate 2.4times risk higher to reduced lung function than adequate indoor fine particles aftercontrolled by ventilation and tobacco smoke exposure. Spatial analysis concludedthat RW 5 and RW 8 Sukadanau, West Cikarang were in priority zone with veryhigh risk area.]"