Fixed point theorems in dislocated quasi-metric spaces
-
3270
Downloads
-
6678
Views
Authors
Shizheng Li
- LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, P. R. China.
- College of Mathematical Sciences, Dezhou University, Dezhou, Shandong 253023, P. R. China.
Akbar Zada
- Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
Rahim Shah
- Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
Tongxing Li
- LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, P. R. China.
- School of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, P. R. China.
Abstract
In this paper, we discuss the existence and uniqueness of a fixed point in a dislocated quasi-metric space. Several
fixed point theorems for distinct type of contractive conditions are presented that generalize, extend, and unify
a number of related results reported in the literature. Illustrative examples are provided.
Share and Cite
ISRP Style
Shizheng Li, Akbar Zada, Rahim Shah, Tongxing Li, Fixed point theorems in dislocated quasi-metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4695--4703
AMA Style
Li Shizheng, Zada Akbar, Shah Rahim, Li Tongxing, Fixed point theorems in dislocated quasi-metric spaces. J. Nonlinear Sci. Appl. (2017); 10(9):4695--4703
Chicago/Turabian Style
Li, Shizheng, Zada, Akbar, Shah, Rahim, Li, Tongxing. "Fixed point theorems in dislocated quasi-metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4695--4703
Keywords
- Dislocated quasi-metric space
- fixed point
- contraction mapping
- self-mapping
- Cauchy sequence.
MSC
References
-
[1]
C. T. Aage, J. N. Salunke, Some results of fixed point theorem in dislocated quasi-metric spaces, Bull. Marathwada Math. Soc., 9 (2008), 1–5.
-
[2]
C. T. Aage, J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Appl. Math. Sci. (Ruse), 2 (2008), 2941–2948.
-
[3]
S. Abramsky, A. Jung , Domain theory, Handbook of logic in computer science, Handb. Log. Comput. Sci., Oxford Sci. Publ., Oxford Univ. Press, New York, 3 (1995), 1–168.
-
[4]
S. Banach , Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , Fund. Math., 3 (1922), 133–181.
-
[5]
B. K. Dass, S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math., 6 (1975), 1455–1458.
-
[6]
P. Hitzler, A. K. Seda, Dislocated topologies, J. Electr. Eng., 51 (2000), 3–7.
-
[7]
A. Isufati , Fixed point theorems in dislocated quasi-metric space, Appl. Math. Sci. (Ruse), 4 (2010), 217–223.
-
[8]
K. Jha, D. Panthi , A common fixed point theorem in dislocated metric space, Appl. Math. Sci. (Ruse), 6 (2012), 4497–4503.
-
[9]
K. Jha, K. P. R. Rao, D. Panthi , A common fixed point theorem for four mappings in dislocated quasi-metric space, Int. J. Math. Sci. Eng. Appl., 6 (2012), 417–424.
-
[10]
D. Panthi, K. Jha, G. Porru, A fixed point theorem in dislocated quasi-metric space, Amer. J. Math. Stat., 3 (2013), 153–156.
-
[11]
S. T. Patel, M. Patel , Some results of fixed point theorem in dislocated quasi metric space, Int. J. Res. Mod. Eng. Technol., 1 (2013), 20–24.
-
[12]
H. Piri , Some Suzuki type fixed point theorems in complete cone b-metric spaces over a solid vector space, Commun. Optim. Theory, 2016 (2016), 15 pages.
-
[13]
M. Sarwar, M. U. Rahman, G. Ali , Some fixed point results in dislocated quasi metric (dq-metric) spaces, J. Inequal. Appl., 2014 (2014), 11 pages.
-
[14]
R. Shrivastava, Z. K. Ansari, M. Sharma, Some results on fixed points in dislocated and dislocated quasi-metric spaces, J. Adv. Stud. Topol., 3 (2012), 25–31.
-
[15]
F. M. Zeyada, G. H. Hassan, M. A. Ahmed, A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces, Arab. J. Sci. Eng. Sect. A Sci., 31 (2006), 111–114.
-
[16]
K. Zoto, E. Hoxha, A. Isufati, Some new results in dislocated and dislocated quasi-metric spaces, Appl. Math. Sci. (Ruse), 6 (2012), 3519–3526.
-
[17]
K. Zoto, S. Radenović,, J. Dine, I. Vardhami , Fixed points of generalized (\(\psi,s,\alpha\))-contractive mappings in dislocated and b-dislocated metric spaces, Commun. Optim. Theory, 2017 (2017), 16 pages.