Fixed Point Theorems in Complex Valued B-Metric Spaces

Dahliatul Hasanah

Abstract


A complex-valued b-metric space is a generalization of a b-metric space in which its b-metric space has complex value. It can also be considered as a generalization of a complex-valued metric space. Hence, fixed point theorems that have been studied in b-metric spaces are now of interest whether the theorems are applicable in complex-valued b-metric spaces. In this paper we have obtained some fixed point theorems in complex-valued b-metric spaces. The theorems are derived from the corresponding theorems in b-metric spaces.

Keywords


b-metric spaces, complex valued b-metric spaces, fixed point theorems

Full Text:

PDF

References


T. Zamfirescu, “Fix point theorems in metric spaces”, Archiv der Mathematik, vol. 2, no. 1, pp. 292-298, December 1972.

G. Emmanuele, “Fixed point theorems in complete metric spaces”, Nonlinear Analysis: Theory, Methods & Applications. Great Britain, vol. 5, no. 3, pp. 287-292, 1981.

T. Suzuki, “A new type of fixed point theorem in metric spaces”, Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 11, pp. 5313-5317, December 2009.

I. A. Bakhtin, “The contraction principle in quasimetric spaces”, Functional Analysis, vol. 30, pp. 26-37, 1989.

P. K. Misra, S. Sachdeva, and S. K. Banerjee, “Some fixed point theorems in b-metric space”, Tourkish Journal of Analysis and Number Theory, vol. 2, no. 1, pp. 19-22, 2014.

A. K. Dubey, R. Shukla, and R. P. Dubey, “Some fixed point results in b-metric spaces”, Asian Journal of Mathematics and Applications, vol. 2014, 2014.

M. Demma and P. Vetro, “Picard sequence and fixed point results on b-metric spaces”, Hindawi Publishing Corporation. Journal of Function Spaces, vol. 2015, 2015.

http://dx.doi.org/10.1155/2015/189861.

A. Azzam, B. Fisher, and M.Khan, “Common fixed point theorems in complex valued metric spaces”, Numerical Functional Analysis and Optimization. Philadelphia, vol. 32, no. 3, pp. 243-253, 2011.

K. Sitthikul and S. Saejung, “Some fixed point theorems in complex valued metric spaces”, Fixed Point Theory and Applications, 2012:189.

W. Sintunavarat and P. Kumam, “Generalised common fixed point theoremsin complex valued metric spaces and applications”, Journal of Inequalities and Applications. 2012.

H. K. Nashine, M. Imdad, and M. Hasan, “Common fixed point theorems under rational contractions in complex valued metric spaces”, Journal of Nonlinear Science and Applications, vol. 7, pp. 42-50, 2014.

A. A. Mukheimer, “Some common fixed point theorems in complex valued b-metric spaces”, Hindawi Publishing Coorporation. The Scientific World Journal, vol. 2014, 2014.

http://dx.doi.org/10.1155/2014/587825.

A. K. Dubey, R. Shukla, and R. P. Dubey."Some fixed point theorems in complex valued b-metric spaces", Hindawi Publishing Corporation. Journal of Complex Systems, vol. 2015, 2015. http://dx.doi.org/10.1155/2015/832467

M. Kir and H. Kiziltunc, "On some well known fixed point b-metric spaces", Turkish Journal of Analysis and Number Theory , vol. 1, no. 1, pp.13-16, 2013.




DOI: https://doi.org/10.18860/ca.v4i4.3669

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Dahliatul Hasanah

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.