Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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COMMON FIXED POINT THEOREMS UNDER RATIONAL CONTRACTIONS IN COMPLEX VALUED EXTENDED b-METRIC SPACES

  • Vairaperumal, V. (PG and Research Department of Mathematics, St.Josephs College(Autonomous)) ;
  • Raj, J. Carmel Pushpa (PG and Research Department of Mathematics, St.Josephs College(Autonomous)) ;
  • Joseph, J. Maria (PG and Research Department of Mathematics, St.Josephs College(Autonomous)) ;
  • Marudai, M. (Department of Mathematics, Bharathidasan University)
  • Received : 2021.01.09
  • Accepted : 2021.04.03
  • Published : 2021.12.15
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Abstract

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

Keywords

Acknowledgement

The authors would like to thank the editor of the journal and the referees for their precise remarks to improve the presentation of the paper.

References

  1. A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric Spaces, Num. Funct. Anal. Opti., 32(3) (2011), 243-253. https://doi.org/10.1080/01630563.2011.533046
  2. I.A. Bakhtin, The contraction principle in quasi metric spaces, In: Functional Analysis, 30 (1989), 26-37.
  3. S. Banach, Sur les, operations dans les ensembles abstraits et leur application aux equations integrales, Fundam. Math., 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  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), 1-14.
  5. S. Czerwik, Nonlinear set-valued contractions mappings in b-metric spaces, Atti del Semi- nario Matematico e Fisico dell Universita di Modena, 46(2) (1998), 263-276.
  6. D. Dayana Roselin, J. Carmel Pushpa Raj and J.M. Joseph, Fixed Point and Common Fixed Point Theorems on Complex Valued b-metric spaces, Infokara Research, 8(9) (2019), 882-892.
  7. A.K. Dubey, Complex valued-metric Spaces and common fixed point theorems under rational contractions, J. Complex Anal., 2016.
  8. 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. https://doi.org/10.1016/j.jmaa.2005.03.087
  9. J.M. Joseph, D.D. Roselin and M. Marudai, Fixed point theorems on multivalued mappings in b-metric spaces, SpringerPlus, 5 217 (2016). https://doi.org/10.1186/s40064-016-1870-9
  10. T. Kamran, M. Samreen and Q. UL Ain, A Generalization of b-metric space and some fixed point theorems, Mathematics, 5(2): 19 (2017). https://doi.org/10.3390/math5020019
  11. A.A. Mukheimer, Some common fixed point theorems in complex valued b-metric spaces,The Scientific World J., 2014 (2014), Article ID 587825, 6 pages.
  12. S.B. Nadler, Multi-valued contraction mappings, Pac. J. Math, 30 (1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475
  13. K.P.R. Rao, P.R. Swamy and J.R. Prasad, A common fixed point theorem in Complex Valued b-metric spaces, Bull. Math. Statis. Research, 1(1) (2013), 1-8.
  14. N. Ullah, M.S. Shagari and A. Azam, Fixed point theorems in Complex valued extended b-metric spaces, Moroccan J. Pure and Appl. Anal., 5(2) (2019), 140-163. https://doi.org/10.2478/mjpaa-2019-0011