Anil Kumar Dubey* | Mithilesh Deo Pandey | Ravi Prakash Dubey
OPEN ACCESS
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.
common fixed point, normal cone, c-Distance
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.
[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.