A fixed point theorem for mappings with an F-contractive iterate

Yıl 2019, Cilt: 3 Sayı: 4, 231 - 236, 30.12.2019

Ali Öztürk

https://doi.org/10.31197/atnaa.644325

Cited By: 6

Öz

In this paper, we introduce the notion of $F$-contraction in the setting of complete metric space and we prove a fixed point theorem for $F$-contractive iteration.

Anahtar Kelimeler

F-contraction, Fixed point, Complete metric space, Contractive iteration

Kaynakça

• M. Abbas, M. Berzig, T. Nazir, E. Karapinar, Iterative Approximation of Fixed Points for Presic Type F-Contraction Operators,University Politehnica Of Bucharest Scientific Bulletin-Series A-Applied Mathematics And Physics, 78(2) (2016), 147-160.
• B. Alqahtani, A. Fulga, E. Karapinar, A fixed point result with a contractive iterate at a point, Mathematics, 7(7) (2019), 606.
• B. Alqahtani, A. Fulga, E. Karapinar, P. S. Kumari, Sehgal Type Contractions on Dislocated Spaces, Mathematics, 7(2) (2019), 153.
• B. Alqahtani, A. Fulga, E. Karapınar, Sehgal Type Contractions on b-Metric Space, Symmetry, 10 (2018), 560.
• H. H. Alsulami, E. Karapinar, H. Piri, Fixed Points of Modified F-Contractive Mappings in Complete Metric-Like Spaces, Journal of Function Spaces, 2015 (2015), Article ID 270971, 9 pages.
• H.H. Alsulami, E. Karapınar, F. Khojasteh, A.F. Roldán-López-de-Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dynamics in Nature and Society, Article ID 269286, (2014), 10 pages
• H. Aydi, E. Karapinar, H. Yazidi, Modified F-Contractions via alpha-Admissible Mappings and Application to Integral Equations, Filomat, 31(5) (2017), 1141- 148. S.
• Banach, Sur les op\'{e}rations dans les ensembles abstraits et leur application aux \'{e}quations int\'{e}grales, Fundamenta Mathematicae, 3 (1922), 133--181.
• M. Bota, Fixed point theorems for operators with a contractive iterate in $b$-metric spaces, Stud. Univ. Babes-Bolyai Math. 61(2016), No. 4, 435--442.
• V. W. Bryant, A remark on a fixed point theorem for iterated mappings, The American Mathematical Monthly, vol. 75, pp. 399--400, 1968.
• Lj. B. \'{C}iri\'{c}, On Sehgal's maps with a contractive iterate at a point, Publ. Inst. Math. (Beograd) (N.S.), 33 (47) (1983), 59-62.
• L. F. Guseman, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Am. Math. Soc., 26 (1970), 615-618.
• E. Karapinar, H. Piri and H.H. AlSulami, Fixed Points of Generalized F-Suzuki Type Contraction in Complete b-Metric Spaces, Discrete Dynamics in Nature and Society, 2015 (2015), Article ID 969726, 8 pages.
• E. Karapınar, H. Aydi, A. Fulga, W. Shatanavi, Wardowski type contractions with applications on Caputo type nonlinear fractional differential equations, in press
• F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (6) (2015), 1189-1194
• Z. D. Mitrovi \'{c}, An Extension of Fixed Point Theorem of Sehgal in $b$-Metric Spaces, Commun. Appl. Nonlinear Anal., 25 (2018), Number 2, 54-61.
• A.F. Roldán-López-de-Hierro, E. Karapınar, C. Roldán-López-de-Hierro, J. Martínez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math. 275 (2015), 345–355
• V. M. Sehgal, A fixed point theorem for mappings with a contractive iterate, Proc. Amer. Math. Soc., 23 (1969), 631-634.
• D. Wardowski: Fixed Points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012).