Common Fixed Point Theorems on Cone Metric Spaces With C-Distance

Common Fixed Point Theorems on Cone Metric Spaces With C-Distance

Anil Kumar DubeyMithilesh Deo Pandey Ravi Prakash Dubey 

Department of Applied Mathematics, Bhilai Institute of Technology, Bhilai House, Durg, Chhattisgarh 491001, India

Department of Mathematics, Dr. C. V. Raman University, Kota, Bilaspur, Chhattisgarh 495113, India

Corresponding Author Email: 
anilkumardby70@gmail.com
Page: 
196-200
|
DOI: 
https://doi.org/10.18280/ama_a.550403
Received: 
18 May 2018
| |
Accepted: 
15 October 2018
| | Citation

OPEN ACCESS

Abstract: 

The purpose of this paper is to prove common fixed point theorems by using the c-Distance in a cone metric space with different types of contractive conditions. Our theorem extends the contractive condition from constant real numbers to some control functions.

Keywords: 

common fixed point, normal cone, c-Distance

1. Introduction
2. Main Result
3. Conclusion
Acknowledgment

The authors are thankful to the learned referee for his/her deep observations and their suggestions which greatly helped us to improve the paper significantly.

  References

[1] Dubey AK, Verma R, Dubey RP. (2015). Cone Metric Spaces and Fixed Point Theorems of Contractive Mapping for c-Distance. International Journal of Mathematics and Its Applications 3(1): 83-88. https://doi.org/10.1007/s10114-010-8019-5

[2] Dubey AK, Mishra U. (2016). Some fixed point results of single-valued mapping for c-distance in tvs-cone metric spaces. Filomat 30(11): 2925-2934. https://doi.org/10.2298/FIL1611925D

[3] Dubey AK, Mishra U. (2017). Some fixed point results for c-distance in cone metric spaces. Nonlinear Functional Analysis and Application 22(2): 275-286.

[4] Dubey AK, Verma R, Dubey RP. (2015). Coupled fixed point results with c-distance in cone metric spaces. Asia Pacific Journal of Mathematics 2(1): 20-40. 

[5] Kaewkhao A, Sintunavarat W, Kumam P. (2012). Common fixed point theorems of c-distance on cone metric spaces. Journal of Nonlinear Analysis and Application 2012(jnaa-00137): 11. https://doi.org/10.1186/1687-1812-2012-194

[6] Jungck G, Radenovic S, Radojevic S, Rakocevic V. (2009). Common fixed point theorems for weakly compatible pairs on cone metric spaces. Fixed Point Theory and Applications 2009(643840). https://doi.org/10.1155/2009/643840

[7] Rahimi H, Rad GS, Kumam P. (2015). A generalized distance in a cone metric space and new common fixed point results. U.B.P.Sci. Bull. Series A 77(2): 195-206.

[8] Rahimi H, Rhoades BE, Radenovic S, Rad GS. (2013). Fixed and periodic point theorems for T-contractions on cone metric spaces. Filomat 27(5): 881-888. https://doi.org/110.2298/FIL1305881R

[9] Rahimi H, Soleimani Rad G. (2013). Note on “common fixed point results for non commuting mappings without continuity in cone metric spaces. Thai J. Math 11(3): 589-599.

[10] Rahimi H. (2013). Some common fixed point results for weakly compatible mappings in cone metric type space. Miskolc Mathematical Notes 14(1): 233-243. https://doi.org/doi:10.1155/2013/939234

[11] Huang LG, Zhang X. (2007). Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl 332: 1467-1475. https://doi.org/10.1016/j.jmaa.2005.03.087

[12] Abbas M, Jungck G. (2008). Common fixed point results for non commuting mappings without continuity in cone metric spaces. J. Math. Anal. Appl. 341: 416-420. https://doi.org/10.1016/j.amc.2009.04.085

[13] Kada O, Suzuki T, Takahashi W. (1996). Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Math. Japon 44: 381-391.

[14] Wang S, Guo B. (2011). Distance in cone metric spaces and common fixed point theorems. Applied Mathematical Letters 24: 1735-1739. https://doi.org/10.1016/j.aml.2011.04.031

[15] Sintunavarat W, Cho YJ, Kumam P. (2011). Common fixed point theorems for c-distance in ordered cone metric spaces. Comput. Math. Appl 62: 1969-1978.

[16] Cho YJ, Saadati R, Wang SH. (2011). Common fixed point theorems on generalized distance in ordered cone metric spaces. Comput. Math. Appl 61: 1254-1260. https://doi.org/10.1016/j.camwa.2011.01.004

[17] Yang YO, Choi HJ. (2018). Fixed point theorems on cone metric spaces with c-distance. J. Computational Analysis and Applications 24(5): 900-909.