On Double Controlled Metric-Like Spaces and Related Fixed Point Theorems

Yıl 2021, Cilt: 5 Sayı: 2, 167 - 172, 30.06.2021

Ayşegül Taş

https://doi.org/10.31197/atnaa.869586

Cited By: 4

Öz

In this paper, we generalize the fixed point theorem given in Mlaiki et al [Journal of Inequalities and
Applications (2020) 2020:63] using the concept of double controlled metric-like spaces.
Some examples are given here to illustrate the usability of the obtained results.

Anahtar Kelimeler

b-metric spaces, double controlled metric space, fixed point

Kaynakça

• Bakhtin, I.A. The contraction mapping principle in almost metric spaces. Funct. Anal. 1989, 30, 26–37.
• S. Czerwik, Contraction mappings in b-metric spaces, Acta mathematica et informatica universitatis ostraviensis, vol. 1, pp. 5–11, 1993.
• T. Kamran, M. Samreen, and Q. UL Ain, A generalization of b-metric space and some fixed point theorems, Mathematics, vol. 5, no. 2, p. 19, 2017.
• N. Mlaiki, H. Aydi, N. Souayah, and T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics, vol. 6, no. 10, p. 194, 2018.
• N. Mlaiki, Double controlled metric-like spaces, Journal of Inequalities and Applications, (2020) 2020:189
• T. Abdeljawad, N. Mlaiki, H. Aydi, and N. Souayah, Double controlled metric type spaces and some fixed point results, Mathematics, vol. 6, no. 12, p. 320, 2018.
• Abdeljawad, T., Karapinar, E., Tas, Kenan; Existence and Uniqueness of aCommon Fixed point on Partial Metric Spaces, Applied Mathematics Letters, Vol.24, No: 11, 1900-1904, (2011).
• T Abdeljawad, E Karapınar, K Taş, A generalized contraction principle with control functions on partial metric spaces, Computers andMathematics with Applications 63 (3), 716-719, (2012)
• S. Reich, Fixed point of contractive functions, Bollettino dell'Unione Matematica Italiana, vol. 4, pp. 26–42, 1972.
• E. Karapinar, A Short Survey on the Recent Fixed Point Results on b-Metric Spaces, Constructive Mathematical Analysis, 1 (2018), No. 1, pp. 15-44
• U.Aksoy, E. Karapinar and I. M. Erhan, Fixed points of generalized alpha-admissible contractions on b-metric spaces with an application to boundary value problems,Journal of Nonlinear and Convex Analysis, (2016). Volume 17,Number 6, 1095-1108
• H. H. Alsulami, E. Karapinar, V. Rakocevic Ciric Type Nonunique Fixed Point Theorems on b-Metric Spaces, Filomat 31:11 (2017), 3147-3156
• E. Karapinar, H. Piri and H. Al Sulami, Fixed Points of Generalized F-Suzuki Type Contraction in Complete bMetric Spaces„" Discrete Dynamics in Nature and Society, 2015 (2015), Article ID 969726, 8 pages
• H. Guan, J. Li, Common Fixed-Point Theorems of Generalized $(\psi,\phi)$-Weakly Contractive Mappings in b-Metric-Like Spaces and Application, Journal of Mathematics Volume 2021, Article ID 6680381, 14 pages https://doi.org/10.1155/2021/6680381
• T. Kanwal, A. Hussain, P. Kumam, and E. Savas, Weak partial b-metric spaces and Nadler’s theorem, Mathematics, vol. 7, no. 4, p. 332, 2019.
• Huang, H.; Deng, G.; Radevovic, S. Fixed point theorems in b-metric spaces with applications to differential equations. J. Fixed Point Theory Appl. 2018
• R. Kannan, Some results on fixed points. Bull. Calcutta Math. Soc. 1968, 60, 71–76.
• J. Ahmad, A.E.Al-Mazrooci, H. Aydi, M. De la Sen, On Fixed Point Results in Controlled Metric Spaces, Journal of Function Spaces Volume 2020, Article ID 2108167, 7 pages