INTEGRAL-M_alpha FUNGSI BERNILAI DI RUANG BANACH

Mudzakar Rifal Alam, Prof. Dr. Ch Rini Indrati, M.Si.

2024 | Tesis | S2 Matematika

Di dalam tesis ini dibahas definisi dan karakteristik integral-M_alpha fungsi bernilai di ruang Banach pada [a, b]. Pembahasan dimulai dengan membuktikan eksistensi partisi delta-fine M_alpha pada [a, b]. Berdasarkan partisi tersebut, didefinisikan integral-M_alpha bernilai di ruang Banach. Selanjutnya, dibahas definisi dan karakteristik fungsi primitif-M_alpha dan diperoleh bahwa fungsi primitif-M_alpha memiliki sifat ACG_alpha. Pada bagian akhir, dibangun teorema kekonvergenan untuk integral-M_alpha fungsi bernilai bernilai di ruang Banach.

In this thesis, we discuss the definition and some characteristics of the M_alpha-integral of Banach-valued functions on [a, b]. The discussion will be started by proving the delta-fine M_alpha partition of [a, b]. Based on this partition, we define the M_alpha-integral of Banach-valued functions. Furthermore, we discuss the definition and characteristics of primitive-M_alpha functions and the result is that the primitive-M_alpha functions have ACG_alpha properties. In the last discussion, we prove the convergence theorems for M?-integral of Banach-valued functions.

Kata Kunci : Integral M_\alpha, partisi delta-fine, primitif-M_alpha, ruang Banach