Fixed point theorems in rational form via Suzuki approaches

Yıl 2018, Cilt: 1 Sayı: 1, 19 - 29, 24.04.2018

Andreea Fulga

https://izlik.org/JA46FB96UJ

Öz

 In this paper we establish some fixed point theorems by using the new contractive
condition, introduced in [11] by T.Suzuki.

Anahtar Kelimeler

Fixed point , contraction of rational type

Kaynakça

• [1] J. Achari, On Ciri´ c’s non-unique fixed points, Mat. Vesnik, 13 (28)no. 3, 255-257 (1976)
• [2] M. Arshad, E. Karapınar, A. Jamshaid, Some unique fixed point theorems for rational contractions in partiallyordered metric spaces. J. Inequal. Appl. 2013, Article ID 248 (2013)
• [3] L.B. Ciric, On some maps with a nonunique fixed point. Publ. Inst. Math. 17, 52-58 (1974).
• [4] B. K. Dass and S. Gupta, An extension of Banach contraction principle through rational expressions, Indian J.Pure Appl. Math., 6(1975), 1455-1458
• [5] D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math, vol. 8, pp. 223-230, 1977
• [6] E. Karapınar, A New Non-Unique Fixed Point Theorem, J. Appl. Funct. Anal. , 7 (2012),no:1-2, 92-97.
• [7] H.Piri, P.Kumam, Some fixed point theorems concerning F−contraction in complete metric spaces, Fixed PoinTheory Appl. 210(2014)
• [8] H.Piri, P.Kumam, Wardowski type fixed point theorems in complete metric spaces, Fixed Point Theory andApplications 20162016:45
• [9] Z. Mustafa, E. Karapınar and H. Aydi, A discussion on generalized almost contractions via rational expressionsin partially ordered metric spaces, Journal of Inequalities and Applications 2014, 2014:219
• [10] A. H. Soliman, Fixed point theorems for a generalized contraction mapping of rational type in symmetricspaces, Journal of the Egyptian Mathematical Society 25(2017), 298-301
• [11] T.Suzuki, Fixed point theorem for a kind of Ciric type contractions in complete metric spaces, Advances inthe Theory of Nonlinear Analysis and its Applications 2(2018) No 1, 33-41
• [12] T. Suzuki, A generalisation of Hegedus-Szilagyi’s fixed point theorem in complete metric spaces, Fixed PointTheory Appl., 2018, 2018:1
• [13] T. Suzuki, A new type of fixed point theorem on metric space, Nonlinear Anal., 71(2009), 5313-5317
• [14] D. Wardowski, Fixed Points of a new type of contractive mappings in complete metric spaces, Fixed PointTheory Appl. 94 (2012).
• [15] D. Wardowski, Van Dung,N.: Fixed points of F-weak contractions on complete metric spaces, DemonstratioMathematica, 2014.