Fixed Point Theorems for T-Contractions with c-Distance on Cone Metric Spaces

Rita Pal, Anil Kumar Dubey, Mithilesh Deo Pandey

Abstract


In this paper, we prove the existence and uniqueness of the fixed point for T-contraction mapping under the concept of c-Distance in cone metric spaces with solid cone. The obtained results extend and generalize well known comparable results in the literature.


Keywords


Cone metric space; Fixed point; T-contraction

Full Text:

PDF

References


M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416 – 420, DOI: 10.1016/j.jmaa.2007.09.070.

M. Abbas and B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. 22 (2009), 511 – 515, DOI: 10.1016/j.aml.2008.07.001.

A. Beiranvand, S. Moradi, M. Omid and H. Pazandeh, Two fixed point theorem for special mapping, arXiv:0903.1504v1[math.FA], url: https://arxiv.org/pdf/0903.1504.pdf.

Y. J. Cho, R. Saadati and S. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comut. Math. Appl. 61 (2011), 1254 – 1260, DOI: 10.1016/j.camwa.2011.01.004.

A. K. Dubey, R. Shukla and R. P. Dubey, Common fixed point theorems for T-reich contraction mapping in cone metric spaces, Advances in Fixed Point Theory 3(2) (2013), 315 – 326, URL: http://www.scik.org/index.php/afpt/article/view/937.

A. K. Dubey, R. Shukla and R. P. Dubey, Common fixed point theorem for generalized T-hardyrogers contraction mapping in a cone metric space, Advances in Inequalities and Applications 2014 (2014), 18, 1 – 16,URL: http://www.scik.org/index.php/aia/article/view/1522.

A. K. Dubey, R. Shukla and R. P. Dubey, Cone metric spaces and fixed point theorems of generalized T-Zamfirescu mappings, International Journal of Applied Mathematical Research 2(1) (2013), 151 – 156, DOI: 10.14419/ijamr.v2i1.650.

A. K. Dubey, R. Verma and R. P. Dubey, Cone metric spaces and fixed point theorems of contractive mapping for c-distance, International Journal of Mathematics And its Applications 3(1) (2015), 83 – 88, URL: http://www.ijmaa.in/papers/3110.pdf.

A. K. Dubey and U. Mishra, Some fixed point results for c-distance in cone metric spaces, Nonlinear Funct. Anal. & Appl. 22(2) (2017), 275 – 286.

A. K. Dubey and U. Mishra, Some fixed point results of single-valued mapping for c-distance in TVS-cone metric spaces, Filomat 30, 11 (2016), 2925 – 2934, DOI: 10.2298/FIL1611925D.

M. Filipovic, L. Paunovic, S. Radenovic and M. Rajovic, Remarks on “Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings”, Math. Comput. Modelling 54 (2011), 1467 – 1472, DOI: 10.1016/j.mcm.2011.04.018.

Z. M. Fadail, A. G. B. Ahmad and L. Paunovic, New fixed point results of single valued mapping for c-distance in cone metric spaces, Abstract and Applied Analysis 2012(2012), Article ID 639713, 1 – 12, DOI: 10.1155/2012/639713.

Z. M. Fadail and S. M. Abusalim, T-Reich contraction and fixed point results in cone metric spaces with c-distance, International Journal of Mathematical Analysis 11(8) (2017), 397 – 405, DOI: 10.12988/ijma.2017.7338.

L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332(2007), 1468 – 1476, DOI: 10.1016/j.jmaa.2005.03.087.

G. Jungck, S. Radenovic, S. Radojevic and V. Rakocevic, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory and Applications 2009 (2009), Article ID 643840, DOI: 1155/2009/643840.

H. Rahimi, B. E. Rhoades, S. Radenovic and G. S. Rad, Fixed and periodic point theorems for T-contractions on cone metric spaces, Filomat 27(5) (2013), 881 – 888, DOI: 10.2298/FIL1305881R.

W. Sintunavarat, Y. J. Cho and P. Kumam, Common fixed point theorems for c-distance in ordered metric spaces, Comput. Math. Appl. 62(2011), 1969 – 1978, DOI: 10.1016/j.camwa. 2011.06.040.

S. Wang and B. Guo, Distance in cone metric spaces and common fixed point theorems, Applied Mathematical Letters 24 (2011), 1735 – 1379, DOI: 10.1016/j.aml.2011.04.031.




DOI: http://dx.doi.org/10.26713%2Fjims.v11i3-4.967

eISSN 0975-5748; pISSN 0974-875X