A note on Kannan type mappings with a F-contractive iterate

Yıl 2019, Cilt: 2 Sayı: 3, 143 - 146, 01.10.2019

Selma Gulyaz-ozyurt

Öz

In this paper, we revisited fixed point theorem for Kannan type mapping  with a contractive iterate at a point in the setting of $F$-construction. The given results extend and improve the related results in the literature.

Anahtar Kelimeler

Fixed point , $b$-metric space , contractive iteration

Kaynakça

• [1] Banach, S. Sur les operations dans les ensembles abstraits et leur application auxequations integrales, Fundamenta Mathematicae, 3 (1922), 133–181.
• [2] Bryant, V. W. A remark on a fixed point theorem for iterated mappings, The AmericanMathematical Monthly, vol. 75, pp. 399–400, 1968.
• [3] L. F. Guseman, Fixed point theorems for mappings with a contractive iterate at a point,Proc. Am. Math. Soc. 26, (1970), 615-618.
• [4] A. Özturk, A fixed point theorem for mappings with an F-contractive iterate, Advancesin the Theory of Nonlinear Analysis and its Applications 3 (2019) No. 3, 231-235.
• [5] V. M. Sehgal, A fixed point theorem for mappings with a contractive iterate, Proc.Amer. Math. Soc., 23 (1969), 631-634.
• [6] D. Wardowski, Fixed Points of a new type of contractive mappings in complete metricspaces, Fixed Point Theory Appl. 94 (2012).