EKSISTENSI DAN KETUNGGALAN TITIK TETAP HARDY DI RUANG B-METRIK LENGKAP - Ahmad Khairul Umam; Pukky Tetralian Bantining Ngastiti; Krisna Adilia Daniswara; Zaqiyatus Shahadah; Amanda Fatma Muamalah (MathVisioN, 2025)
The fixed point is useful not only to solve problems in linear equation and differential equation, but also integral equation. The fixed point theorem of Hardy is generalization of the fixed point theorem of Reich. The metric space can be generalized to other spaces. b-metric space is one of generalization of metric space. Axiom of triangle inequality in metric space is not the same as axiom of triangle inequality in b-metric space. In this research, we discuss about fixed point theorem of Hardy in metric space. Besides that, we also discuss about fixed point of Hardy in complete b-metric space. Before proving that theorem, we prove lemma that supports the proof of theorem. We prove not only existance, but also uniqueness of fixed point from a function defined in complete b-metric space.