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Abstrak :
ABSTRAK
Titik x disebut titik tetap dari pemetaan f jika dan hanya jika f(x) = x, sebagai contoh jika pernetaan f didefinisikan dengan f(x) = x2 - 3x + 4, rnaka 2 adalah titik tetap dari f karena f(2) = 2. Ruang Metrik-G adalah pasangan (X, G) dengan X adalah hirnpunan tak kosong dan G adalah rnetrik (jarak) pada X (didefinisikan pada X >< X >< X) dengan G: X >< X >< X -> RJ? sedemikian hingga untuk setiap x, y, Z, a E X, rnernenuhi syarat berikut: (GI) G(x,y,z) = Ojika x = y = Z, (GZ) 0 < G(x,x,y)dengar1 x i y, (G3) G(x, x, y) 5 G(x, y, z) dengan z 42 y,(G4) G(x, y, Z) = G(x, z, y) = G(y, z,x) = G(y,x, z) = G(z,x,y) = G(z, y, x), (GS) G(x, y,z) S G(x, a, a) + G(a, y, Z). Ruang Metrik-G (X, G) adalah Ruang Metrik-G lengkap jika setiap barisan G-Cauchy di (X, G)adalah G-konvergen di (X, G). Suatu pemetaan T: X -> X pada Ruang Metrik-G lengkap disebut pernetaan kontraktifjika terdapat konstanta lc, 0 S Fc < 1 sedernikian hingga G(T(x), T(y), T(z) S kG(x,y, Z). Tidak sernua pemetaan memiliki titik tetap. Dari hasil penelitian diperoleh sifat-sifat dari Ruang Metrik-G lengkap dan syarat cukup agar diperoleh ketunggalan titik tetap untuk pemetaan kontraktif pada Ruang Metrik-G lengkap.

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Abstract
Point x is called a fixed point ofthe mapping f if and only if f(x) = x, for example ifthe mapping f defined by f(x) = x2 - 3x + 4, then 2 is a fixed point of f because = 2. Metric-G Space is a pair (X, G) Where X is a nonempty set and G is a metric (distance) onX (defined on X X X >< X) with G: X >< X X X -> R+ such that for every x, y, Z, a E X, satisfy the following requirement:(Gl) G (x, y, Z) = 0 ifx = y = z, (GZ) 0 < G(x,x,y) forx 92 y, (G3) G(x,x,y) 5 G(x,y,z) for z ¢ y,(G4) G(x,y,z) = G(x,z,y) = G(y,z,x) = G(y,x,z) = G(z,x,y) = G(z, y, x), (G5) G(x,y, Z) 5 G(x, a, a) + G(a,y, z). Metric-G Space (X, G) is a complete Metric-G Space if every G-Cauchy sequence in (X, G) is G-convergent in (X, G). A mapping T: X -> X on a complete Metric-G Space is called contractive mapping if there are constants lc, 0 5 k < 1, such that G (T(x), T(y), T(z)) S ICG (x, y, Z). Not every mapping has a fixed point, from the research results obtained by the properties ofthe complete Metric-G Space and sufficient condition in order to obtain uniqueness of fixed point for contractive mapping in complete Metric-G Space.

Abstrak :
Pada skripsi ini pembuktian Teorema Fixed-Point Brouwer untuk kasus dimensi dua (pada cakram) melalui Aljabar Topologi akan dijabarkan. Pembuktian dilakukan dengan bantuan Teorema Ketiadaan Retraksi dan Teorema Lapangan Vektor. Selain membahas pembuktian untuk kasus dua dimensi ( 2 B ), pada skripsi ini pembuktian untuk kasus n dimensi ( n B ) juga dijabarkan. Pada skripsi ini teorema-teorema lain seperti hubungan retraksi dengan fixed point, dan hubungan homotopi dengan fixed point juga dibuktikan.

Abstrak :
This is the only book that deals comprehensively with fixed point theorems throughout mathematics. Their importance is due, as the book demonstrates, to their wide applicability. Beyond the first chapter, each of the other seven can be read independently of the others so the reader has much flexibility to follow his/her own interests. The book is written for graduate students and professional mathematicians and could be of interest to physicists, economists and engineers -- Source other than Library of Congress.

Abstrak :
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. ......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.

Abstrak :
Pembelajaran pada jaringan syaraf tiruan (JST)n melibatkan banyak proses komputasi. Kemampuan JST melakukaan klasifikasi dengan benar menggunakan komposisi bobot hasil pembelajaran merupakan representasi keberhasilan pembelajaran.

Abstrak :
Many advances have taken place in the field of combinatorial algorithms since Methods of Mathematical Economics first appeared two decades ago. Despite these advances and the development of new computing methods, several basic theories and methods remain important today for understanding mathematical programming and fixed-point theorems. In this easy-to-read classic, readers learn Wolfe's method, which remains useful for quadratic programming, and the Kuhn-Tucker theory, which underlies quadratic programming and most other nonlinear programming methods. In addition, the author presents multiobjective linear programming, which is being applied in environmental engineering and the social sciences. The book presents many useful applications to other branches of mathematics and to economics, and it contains many exercises and examples. The advanced mathematical results are proved clearly and completely. By providing the necessary proofs and presenting the material in a conversational style, Franklin made Methods of Mathematical Economics extremely popular among students. The addition of a list of errata, new to this edition, should add to the book's popularity as well as its usefulness both in the classroom and for individual study. The book has three chapters: "Linear Programming," "Nonlinear Programming," and "Fixed-Point Theorems." The first and third chapters include the economic equilibrium theorems of von Neumann and of J. F. Nash, while the second chapter includes Kuhn-Tucker theory and Wolfe's simplex algorithm for quadratic programming. The book concludes with easy, elementary proofs of the famous theorems of Brouwer, of Kakutani, and of Schauder. These fundamental results are usually proved only in advanced texts in topology, economic theory, and nonlinear analysis.