RUANG FUNGSI VARIASI TERBATAS-? YANG DIBANGUN OLEH SUATU METRIK MODULAR DAN KEKONTINUAN LIPSCHITZ OPERATOR SUPERPOSISI; ( ?-BOUNDED VARIATION FUNCTION SPACES GENERATED BY A MODULAR METRIC AND LIPSCHITZ CONTINUITY OF SUPERPOSITION OPERATOR )

ALFANIO RI,ZKY ALFANIO ATMOKO, Supama

2016 | Skripsi | FMIPA

In this thesis, we discuss about modular metrics and convex modulars metric on an arbitrary non empty set X. Let w be a modular metric on a non empty set X. Given x0 2 X, the set Xw = fx 2 X : lim ? 1 w(?; x; x0)g is called modular set. Furthermore, if w is a convex modular metric on X, then the modular set Xw is equal to the set fx 2 X : w(?; x; x0); for some ? > 0g. The set Xw is a metric space with respect to the metrik dw, which is a metrik generated by the modular w. Define I as a closed interval in R. On an arbitrary metric semigroup (M; d; +) and an arbitrary abstrak convex cone (M; d;+; :), we define w to be a modular metric on a set of all function mapping I to M denoted by MI . This modular metric w is a bounded-? variation funtion. The modular set Xw can be regarded as set BV?. A concept of modular metric will be applied to spaces BV? and to superposition operators on spaces BV?. xi

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