Teorema Titik Tetap Kontraksi Tipe Banach–Kannan dan Konvergensi Iterasi General Picard–Mann

Syamsuddin Mas’ud

Jurnal Diferensial
Vol 8 No 2 (2026): November 2026

Fixed point theory plays a crucial role in solving problems modeled by differentialequations and nonlinear equations. In many problems, finding exact fixed points analyticallyis difficult, thus numerical algorithms are needed to approximate them. This study investigatesthe convergence of the General Picard-Mann (GPM) iteration scheme for Banach-Kannan typecontraction mappings in Banach spaces. The GPM iteration scheme combines Picard and Manniterations, generalized by performing k iterations. The main results show that Banach-Kannan typecontraction mappings on complete metric spaces have a unique fixed point. Moreover, it is provedthat sequences generated by the GPM iteration scheme converge to this fixed point in Banach spacesunder the assumption α + 2β < 1. This study complements previous works by extending the class ofmappings that can be approximated using the GPM iteration.