Common Fixed Point Results for Contractive Mapping in Complex Valued \(A_b\)-metric Space

Authors

  • Surandra Kumar Tiwari Department of Mathematics, Dr. C. V. Raman University, Kota, Bilaspur, Chhattisgarh
  • Mridusmita Gauratra Department of Mathematics, Dr. C. V. Raman University, Kota, Bilaspur, Chhattisgarh

DOI:

https://doi.org/10.26713/jims.v12i4.1435

Keywords:

\(A_b\)-metric space, Complex valued metric space, Complex valued \(b\)-metric space, Complex valued \(A_b\)-metric space, Common fixed point

Abstract

In this article, we prove common fixed point results for two self mappings in complex valued \(A_b\)-metric space. Our results extend and generalize the common fixed point result of Singh and Singh [15].

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References

M. Abbas, A. Muhammad and A. Azam, Fixed points of asymptotically regular mappings in complexvalued metric space, Georgian Mathematical Journal 2013(2013), DOI: 10.1515/gmj-2013-0013.

M. Abbas, B. Ali and Y. I. Suleiman, Generalized coupled common fixed point results in partially ordered A-metric spaces, Fixed Point Theory and Applications 2015 (2015), Article number 64, DOI: 10.1186/s13663-015-0309-2.

J. Ahmad, A. Azam and S. Saejung, Common fixed point results for contractive mappings in complex valued metric spaces, Fixed Point Theory and Applications 2014 (2014), Article number 67, DOI: 10.1186/1687-1812-2014-67.

J. Ahmad, C. Klin-Eam and A. Azam, Common fixed points for multivalued mappings in complex valued metric spaces with applications, Abstract and Applied Analysis 2013 (2013), Article ID 854965, 12 pages, DOI: 10.1155/2013/854965.

K. S. Anthony and M. R. Singh, Fixed points of complex valued Ab-metric space, Electronic Journal of Mathematical Analysis and Applications 8(1) (2020), 27 – 36, URL: http://math-frac.org/Journals/EJMAA/Vol8(1)_Jan_2020/Vol8(1)_Papers/4.pdf.

A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric spaces, Numerical Functional Analysis and Optimization 32(3) (2011), 243 – 253, URL: https://www.tandfonline.com/doi/abs/10.1080/01630563.2011.533046?journalCode=lnfa20.

V. H. Badshah, V. Bairagi and P. Aklesh, Common fixed point theorems in complex valued metric space, Indian Journal of Mathematics and Mathematical Sciences 13(1) (2017), 291 – 298.

C. Klin-eam and C. Suanoom, Some common fixed-point theorems for generalized-contractive-type mappings on complex-valued metric spaces, Abstract and Applied Analysis 2013 (2013), Article ID 604215, 6 pages, DOI: 10.1155/2013/604215.

M. A. Kutbi, A. Azam, A. Jamshaid and C. Bari, Some coupled fixed points results for generalized contraction in complex valued metric spaces, Journal of Applied Mathematics 2013 (2013), Article ID 352927, 10 pages, DOI: 10.1155/2013/352927.

A. A. Mukheimer, Common fixed point theorems for a pair of mappings in complex valued b-metric spaces, Advances in Fixed Point Theory 4(3) (2014), 344 – 354, URL: http://scik.org/index.php/afpt/article/view/1524.

A. A. Mukheimer, Some common fixed point theorems in complex valued b-metric spaces, The Scientific World Journal 2014 (2014), Article ID 587825, 6 pages, DOI: 10.1155/2014/587825.

S. R. Patil and J. N. Salunke, Common fixed point theorems for weakly compatible maps in complex valued b-metric spaces, Advances in Inequalities and Applications 2016 (2016), 8, URL: http://scik.org/index.php/aia/article/view/2561.

K. P. R. Rao, P. R. Swamy and J. R. Prasad, A common fixed point theorem in complex valued b-metric spaces, Bulletin of Mathematics and Statistics Research 1(1) (2013), 1 - 8, URL: http://www.bomsr.com/BOMSR%201.1/KPR%201-8%20mod.pdf.

F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Computers and Mathematics with Applications 64(6) (2012), 1866 – 1874, DOI: 10.1016/j.camwa.2012.02.063.

K. A. Singh and M. R. Singh, Fixed points of complex valued Ab-metric space, South East Asian Journal of Mathematics and Mathematical Sciences 15(2) (2019), 17 – 30, URL: http://rsmams.org/download/articles/2_15_2_1954209862_PAPER%202,%20FIXED%20POINTS%20OF%20COMPLEX%20VALUED%20Ab-METRIC%20SPACE.pdf.

D. Singh, O. P. Chauhan, N. Singh and V. Joshi, Common fixed point theorems in complex valued b-metric spaces, Journal of Mathematical and Computational Science 5(3) (2015), 412 – 429, URL: http://www.scik.org/index.php/jmcs/article/view/2319.

W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, Journal of Inequalities and Applications 2012 (2012), Article number 84, DOI: 10.1186/1029-242X-2012-84.

W. Sintunavarat, J. C. Yeol and P. Kumam, Urysohn integral equations approach by common fixed points in complex-valued metric spaces, Advances in Difference Equations 2013 (2013), Article number 49, DOI: 10.1186/1687-1847-2013-49.

K. Sitthikul and S. Saejung, Some fixed point theorems in complex valued metric space, Fixed Point Theory and Applications 2012 (2012), Article number 189, DOI: 10.1186/1687-1812-2012-189.

M. Ughade, D. Turkoglu, S. R. Singh and R. D. Daheriya, Some fixed point theorems in Abmetric space, British Journal of Mathematics and Computer Science 19(6) (2016), 1 – 24, URL: https://www.sciencedomain.org/abstract/16952.

R. Uthayakumar and G. A. Prabakar, Common fixed point theorem in cone metric space for rational contractions, International Journal of Analysis and Applications 3(2) (2013), 112 – 118, URL: http://etamaths.com/index.php/ijaa/article/view/83.

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Published

2020-12-31
CITATION

How to Cite

Tiwari, S. K., & Gauratra, M. (2020). Common Fixed Point Results for Contractive Mapping in Complex Valued \(A_b\)-metric Space. Journal of Informatics and Mathematical Sciences, 12(4), 257–269. https://doi.org/10.26713/jims.v12i4.1435

Issue

Vol. 12 No. 4 (2020)

Section

Research Articles

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