COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN COMPLEX VALUED b-METRIC SPACES

Anil Kumar Dubey; Madhubala Kasar; Ravi Prakash Dubey

doi:10.24297/jam.v12i12.5744

Authors

Anil Kumar Dubey Bhilai Institute of Technology, Bhilai House, Durg, Chhattisgarh 491001,
Madhubala Kasar Government Higher Secondary School, Titurdih, Durg, Chhattisgarh 491001, India
Ravi Prakash Dubey Dr. C.V. Raman University, Kota, Bilaspur, Chhattisgarh 495113,

DOI:

https://doi.org/10.24297/jam.v12i12.5744

Keywords:

Complex valued b-metric space, weakly compatible maps, (E.A.) property, (CLRg) property.

Abstract

In this paper, we prove a common xed point theorem for weakly compatible mappings in complex valued b-metric space and also improve the condition of contraction of the results of M. Kumar et al.[7]. Further, we prove common xed point theorems for weakly compatible mappings with (E.A.) property and (CLRg) property.

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Author Biographies

Anil Kumar Dubey, Bhilai Institute of Technology, Bhilai House, Durg, Chhattisgarh 491001,

Department of Mathematics

Ravi Prakash Dubey, Dr. C.V. Raman University, Kota, Bilaspur, Chhattisgarh 495113,

Department of Mathematics

References

[1] M. Aamri and D. El. MoutawaKil, Some new common xed point theorems under strict contractive conditions, J. Math. Anal. Appl. 27(1), 181-
188(2002).
[2] A.Azam, B.Fisher and M. Khan, Common xed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim. 32(3),243-253(2011).
[3] A.K. Dubey, Common xed point results for contractive mappings in com- plex valued b-metric spaces, Nonlinear Funct. Anal. and Appl., Vol.20, No.2, 257-268(2015).
[4] A.K. Dubey, Rita Shukla, R.P. Dubey, Some Fixed Point Theorems in Com- plex Valued b-Metric Spaces, Journal of Complex Systems, Vol. 2015, Article ID 832467, 7 Pages, http.//dx.doi.org/10.1155/2015/832467 .
[5] A.K. Dubey, Rita Shukla, R.P. Dubey, Some common xed point theorems for contractive mappings in complex valued b-metric spaces, Asian Journal of Mathematics and Applications, Vol. 2015, Article ID ama0266,
[6] G. Jungck, Common xed points for non-continuous non-self mappings on non-metric spaces, Far East J. Math. Sci. 4(2), 199-212(1996).
[7] M. Kumar, P. Kumar, S. Kumar, Common xed point theorems in Complex valued metric spaces, Journal of Analysis & Number Theory, 2(2), 103-109(2014).
[8] S. Kumar, M. Kumar, P. Kumar, S.M. Kang, Common xed point theorems for weakly compatible mappings in complex valued metric spaces, Int. J. of Pure and Applied Mathematics, 92(3), 403-419(2014).
[9] A.A. Mukheimer, Some common xed point theorems in complex valued b-metric spaces, The Scientic World Journal, Vol.2014(2014), Article ID 587825, 6 pages.
[10] K.P.R Rao, P.R Swamy, J.R., Prasad, A common xed point theorem in complex valued b-metric spaces, Bulletin of Mathematics and Statistics Research, Vol. 1, Issue 1,1-8(2013).
[11] R.K. Verma, H.K. Pathak, Common xed point theorems using property (E.A.) in complex valued metrid spaces, Thai J. of Mathematics, 11(2), 347-355(2013).
[12] W. Sintunavarat, P. Kumam, Common xed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, Journal of Applied Mathematics, 2011, Article ID 637958, 14 pages.
[13] W. Sintunavarat, P. Kumam, Generalized common xed point theorems in complex valued metric spaces and applications, Journal of Inequalities and Applications, (2012), 2012:84
[14] W. Sintunavarat, Y.J. Cho, P. Kumam, Urysohn integral equations ap- proach by common xed points in complex valued metric spaces, Advan ces in Dierence Equations, 2013(2013):49.