Some Fixed Point Theorems for Cyclic Mapping in a Complete B-metric-like Space

Abstract

In recent years, the research of fixed point theorem is a hot topic all the time. In this paper, we proposed the notion of a new mapping, that is, a general LW-type Lipschitz cyclic mapping, in complete b-metric-like spaces. Then, we obtained the existence and uniqueness theorems of its fixed point. Moreover, we give some examples to illustrate the main results in this paper. . .

Keywords

• b-metric-like space
• fixed point theorem
• cyclic mapping

Kaynakça

1. [1] S.G. Matthews, Partial metric topology. In: Proc. 8th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci., vol. 728, pp. 183-197 (1994).
2. [2] A.H. Amini, Metric-like spaces, partial metric spaces and fixed points. J. Fixed Point Theory Appl. 2012, Article ID204 (2012).
3. [3] S. Czerwik, Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostrav. 1, 5-11 (1993).
4. [4] Alghamdi et al.: Fixed point and coupled fixed point theorems on b-metric-like spaces. J. Ine. App. 2013, 2013(1):402.
5. [5] S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fundamenta Mathematicae,3(1922), 133-181.
6. [6] M. Lei, D.P. Wu, Fixed Point Theorems Concerning New Type Cyclic Maps in Complete B-metric-like Spaces, J.Chengdu University Inf Tec. 1.32(2017):82-85.
7. [7] Sh. Weng, Y. Zhang, D.P. Wu, Fixed Point Theorems of LW-Type Lipschitz Cyclic Mappings in Complete B-Metric-Like Spaces, Int.J.Res.Ind.Eng.Vol.7,No.2(2018)136-146.
8. [8] S.Q. Weng, Some Fixed Point Results Involving a General LW-Type Cyclic Mapping in Complete B-Metric-Like Spaces, Int.J.Res.Ind.Eng.Vol.8,No.3(2019) 262-273.

9. [9] H. Aydi, A. Felhi, S. Sahmim, On common fixed points for (α,ψ)-contractions and generalized cyclic contractions in b-metric-like spaces and consequences. J.Nonlinear. Sci. Appl, 9(2016)2492-2510.
10. [10] H.K. Nashinea, Z. Kadelburg, Existence of Solutions of Cantilever Beam Problem via (α − β − FG)-Contractions in b-Metric-Like Spaces. Filomat 31,11 (2017), 3057-3074.
11. [11] A. Fulga, E. Karapinar, G.Petrusel, On Hybrid Contractions in the Context of Quasi-Metric Spaces, Mathemat- ics,8(2020),675.
12. [12] C. Chifu, E. Karapinar, G. Petrusel, Fixed point results in varepsilon-chainable complete b-metric spaces, J.Fixed Point Theory, Volume 21, No.2,2020, 453-464, July 1st, 2020.
13. [13] E. Karapinar, C. Chifu, Results in wt-Distance over b-Metric Spaces, Mathematics,8(2020),220.