Fixed Point Results for ω-Interpolative Chatterjea Type Contraction in Quasi-Partial b-Metric Space

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Pragati Gautam, Swapnil Verma, Manuel De La Sen, Sejal Sundriyal

Abstract

The purpose of this paper is to revisit Chatterjea type contraction and determine some fixed point results for interpolative Chatterjea type contraction mapping in the setting of quasi-partial b-metric space using the concept of ω-admissibility introduced by Popescu. Also we present some useful examples to elucidate relevance of the concept.

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References

  1. S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1922), 133-181.
  2. R. Kannan, Some results on fixed points-II, Amer. Math. Mon. 76 (1969), 405-408.
  3. E. Karapinar, Revisiting the Kannan Type Contractions via Interpolation, Adv. Theory Nonlinear Anal. Appl. 2 (2018), 85-87.
  4. A. Gupta, P. Gautam, Some coupled fixed point theorems on quasi-partial b-metric spaces, Int. J. Math. Anal. 9 (2015), 293-306.
  5. I.A. Bakhtin, The contraction principle in quasi metric spaces, Funct. Anal. 30 (1989), 26-37.
  6. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5-11.
  7. S.G. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728 (1994), 183-197.
  8. S.K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulg. Sci. 25 (1972), 727-730.
  9. P. Gautam, V.N. Mishra, R. Ali, S. Verma, Interpolative Chatterjea and cyclic Chatterjea contraction on quasi-partial b-metric space, AIMS Math. 6 (2020), 1727-1742.
  10. O. Popescu, Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. 2014 (2014), 190.
  11. E. Karapinar, I.M. Erhan, A. Ozt ¨urk, Fixed point theorems on quasi-partial metric spaces, Math. Comput. Model. 57 ¨ (2013), 2442-2448.
  12. A. Gupta, P. Gautam, Quasi-partial b-metric spaces and some related fixed point theorems, Fixed Point Theory Appl. 2015 (2015), 18.
  13. V.N. Mishra, L.M. S ´anchez Ruiz, P. Gautam, S. Verma, Interpolative Reich-Rus-Ciri ´c and Hardy-Rogers Contraction on ´ Quasi-Partial b-Metric Space and Related Fixed Point Results, Mathematics. 8 (2020), 1598.
  14. P. Gautam, L.M. S ´anchez Ruiz, S. Verma, Fixed Point of Interpolative Rus-Reich-Ciri ´c Contraction Mapping on Rectan- ´ gular Quasi-Partial b-Metric Space, Symmetry. 13 (2021), 32.
  15. P. Gautam, S. Verma, Fixed point via implicit contraction mapping on quasi-partial b-metric space, J. Anal. (2021). https://doi.org/10.1007/s41478-021-00309-6.