HUBUNGAN KETAKSAMAAN SEGITIGA DAN KETAKSAMAAN CAUCHY-SCHWARZ MENGGUNAKAN SEMI INNER PRODUK TAPIA

Silvia Rachmawati, NIM.: 20106010040 (2024) HUBUNGAN KETAKSAMAAN SEGITIGA DAN KETAKSAMAAN CAUCHY-SCHWARZ MENGGUNAKAN SEMI INNER PRODUK TAPIA. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

Triangle inequality and Cauchy-Schwarz inequality have been developed by many researchers especially in the aspect of analytical mathematics. This thesis discusses some inequalities obtained from the triangle inequality in normed spaces. The results obtain two inequalities which are another form of the Clarkson distance and a special form of the Maligranda inequality. The role of Tapia’s semi inner product in obtaining the Cauchy-Schwarz inequality in normed spaces is also presented in this thesis. The results are used to analyze the relationship between triangle inequality and Cauchy-Schwarz inequality in inner product spaces. In addition, Tapia’s semi inner product also contributes to form another representation of the Cauchy-Schwarz inequality in inner product spaces.

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