Beberapa Perumuman Kontraksi Kannan di Ruang Metrik Klasik yang Terkait Konsep Titik Tetap
Keywords:
Fixed Point, Kannan Contraction, Classical Metrik Space, GeneralizationAbstract
The Kannan contraction (1968) guarantees the existence of a fixed point without continuity, unlike the Banach principle. This article reviews seven generalizations of Kannan contractions in classical metrik spaces, namely m-Kannan (2025), Hardy-Rogers (1973), mutual Kannan (2022), contraction with auxiliary mapping (2011), F-Kannan (2020), condensed Kannan (2025), and multiplicative Kannan (2025). Each generalization is presented with its definition and explicit reduction conditions to the classical Kannan contraction. Based on the classification of mathematical approaches, the generalizations show an evolution from linear toward nonlinear forms. Three of the seven classes were published in 2025, indicating that this topic remains actively researched. As a contribution, this article maps the seven classes within a single unified framework and presents explicit reduction conditions for each. Several opportunities for further research are also identified, such as extensions to generalized metrik spaces and studies on convergence rates.
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