Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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FIXED POINT THEOREMS IN b-METRIC AND EXTENDED b-METRIC SPACES

  • P. Swapna (Department of Mathematics, JNTUH(MVSR Engineering College)) ;
  • T. Phaneendra (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology) ;
  • M. N. Rajashekhar (Department of Mathematics, JNTUH)
  • Received : 2023.01.19
  • Accepted : 2023.05.29
  • Published : 2023.12.15
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Abstract

The first result of this paper is to give a revised proof of Sanatammappa et al.'s recent result in a b-metric space, under appropriate choice of constants without using the continuity of the b-metric. The second is to prove a fixed point theorem under a contraction type condition in an extended b-metric space.

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Acknowledgement

The authors express sincere thanks to the referees for their useful suggestions in improving the paper.

References

  1. I.A. Bakhtin, The contraction mapping principle in quasi-metric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst., 30 (1989), 26-37.
  2. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis. 1 (1993), 511.
  3. T. Kamran, M. Samreen and Q.Ul. Ain, A generalization of b-metric space and some fixed point theorems, Mathematics, 5(19) (2017), DOI: 10.3390/math5020019.
  4. J.R. Roshan, N. Shobkolaei, S. Sedghi and M. Abbas, Common fixed point of four maps in b-metric spaces, Hacettepe J. Math. and Statistics, 43(4) (2014), 613-624.
  5. W. Rudin, Principles of Mathematical Analysis, McGraw-Hill Int. Edn. Third Edition, 1976.
  6. N.P. Sanatammappa, R. Krishnakumar and K. Dinesh, Some results in b-metric spaces, Malaya J. Matematik, 9(1) (2021), 539-541.
  7. Sonam, C. S. Chauhan, Ramakant Bharadwaj and Satyendra Narayan, Fixed point results in soft rectangular b-metric space, Nonlinear Funct. Anal. Appl., 28(3) (2023), 753-774.
  8. T. Stephen, Y. Rohen, M. K. Singh and K. S. Devi, Some rational F-contractions in b-metric spaces and fixed points, Nonlinear Funct. Anal. Appl., 27(2) (2022), 309-322
  9. B. Wu, F. He and T. Xu, Common fixed point theorems for Ciric type mappings in b-metric spaces without any completeness assumption, J. Nonlinear Sci. Appl., 10 (2017), 3180-3190.