Common fixed point theorems under rational contractions in complex valued extended $b$-metric spaces

Document Type : Research Paper

Authors

1 Department of Mathematics, St. Joseph's College (Autonomous), Tiruchirappalli-620 002, Tamil Nadu, India

2 Department of Mathematics, Bharathidasan University, Tiruchirappalli-620 024, Tamil Nadu, India

Abstract

In this paper, we discuss the existence and uniqueness of fixed point and common fixed point theorems in complex-valued extended b-metric space for a pair of mappings satisfying some rational contraction conditions which generalize and unify some well known results in the literature.

Keywords

[1] A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric Spaces, Numer. Funct.
Anal. Optim. 32(3) (2011) 243–253.
[2] I. Bakhtin, The contraction principle in quasi metric spaces, Funct. Anal. 30 (1989) 26–37.
[3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund.
Math. 3(1) (1922) 133–181.
[4] M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metric spaces, Stud.
Univ. Babes-Bolyai Math. LIV (3) (2009).
[5] C. Pushpa Raj J, V. Vairaperumal, J. Maria Joseph and E. Ramganesh, Common fixed point theorem for mapping
with the generalized weakly contractive conditions in metric spaces, J. Math. Comput. Sci. 10(3) (2020) 572–583.
[6] C. Pushpa Raj J, V. Vairaperumal, J. Maria Joseph and E. Ramganesh, Fixed point and common fixed point
theorems in complex valued b-metric spaces, Adv. Math. Sci. J. 8(3) (2019) 772–780.
[7] S. Czerwik, Nonlinear set-valued contractions mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena.
46 (1998) 263–276.
[8] A.K. Dubey, Complex valued-metric Spaces and common fixed point theorems under rational contractions, J.
Complex Anal. 2016 (2016).
[9] L.G. Huang, and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal.
Appl. 332(2) (2007) 1468–1476.
[10] J.M. Joseph, D.D. Roselin and M. Marudai, Fixed point theorems on multivalued mappings in b-metric spaces,
SpringerPlus 5(1) (2016) 1–8.
[11] T. Kamran, M. Samreen and Q. UL Ain, A generalization of b-metric space and some fixed point theorems, Math.
5(2) (2017) 19
[12] A.A. Mukheimer, Some common fixed point theorems in complex valued b-metric spaces, Sci. World J. 2014 (2014).
[13] S.B. Nadler Jr, Multi-valued contraction mappings, Pac. J. Math. 30(2) (1969) 475–488.
[14] K. Rao, P.R. Swamy and J.R. Prasad. A common fixed point theorem in Complex Valued b-metric spaces, Bull.
Math. Statist. Res. 1(1) (2013) 1–8.
[15] D.D. Roselin, J. Carmel Pushpa Raj, J.M. Joseph, Fixed point and common fixed point theorems on complex
valued b-metric spaces, Infokara Res. 8(9) (2019) 882–892
[16] N. Ullah, M. S. Shagari and A. Azam, Fixed point theorems in Complex valued extended b-metric spaces, Moroccan
J. Pure Appl. Anal. 5(2) (2019) 140–163.
Volume 13, Issue 1
March 2022
Pages 3479-3490
  • Receive Date: 12 March 2020
  • Revise Date: 07 August 2020
  • Accept Date: 28 September 2020