On ω-Interpolative Berinde Weak Contraction in Quasi-Partial b-Metric Space

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Pragati Gautam
Swapnil Verma
Manuel De La Sen
Prachi Rakesh Marwaha

Abstract

The aim of this paper is to introduce interpolative weak contraction in the notion of Berinde weak operator in quasi-partial b-metric space and to extend and generalize fixed point results by adopting the condition of ω-admissibility. We also discussed convex contraction mapping and obtained a fixed point result in the setting of Berinde weak operator in quasi-partial b-metric space. Consequently, we present some examples to show the applicability 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. S. G. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728 (1994), 183-197.
  3. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5-11.
  4. R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 2153-2163.
  5. S. Oltra, O. Valero, Banach's fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste, 36 (2004), 17-26.
  6. O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol. 6(2) (2005), 229-240.
  7. E. Karapinar, I.M. Erhan, A. Ozturk, Fixed point theorems on quasi-partial metric spaces, Math. Comput. Model. 57 ¨ (2013), 2442-2448.
  8. S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math. 11 (2014), 703-711.
  9. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71-76.
  10. V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum. 9(1) (2004), 43-53.
  11. M. Abbas, D. Ilic, Common fixed points of generalized almost non expansive mappings, Filomat. 24(3) (2010), 11-18.
  12. V. Berinde, Some remarks on a fixed point theorem for Ciri`c type almost contractions, Carpathian J. Math. 25(2) (2009), ` 157-162.
  13. I. Altun, O. Acar, Fixed point theorems for weak contractions in the sense of Berinde on partial metric spaces, Topol. Appl. 159(10-11) (2012), 2642-2648.
  14. A. D. T. Turkoglu, V. Ozturk, Common fixed point results for four mappings on partial metric spaces, Abstr. Appl. Anal. 2012 (2012), 190862.
  15. E. Karapinar, Revisiting the Kannan type contractions via interpolation, Adv. Theory Nonlinear Anal. Appl. 2 (2018), 85-87.
  16. C. Boateng Ampadu, Some fixed point theory results for the interpolative Berinde weak operator, Earthline J. Math. Sci. 4(2) (2020), 253-271.
  17. O. Popescu, Some new fixed point theorems for α-Geraghty contractive type maps in metric spaces, Fixed Point Theory Appl. 2014 (2014), 190.
  18. B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α - ψ-contractive type mappings, Nonlinear Anal., Theory Meth. Appl. 75 (2012), 2154-2165.
  19. H. Aydi, E. Karapinar, A. F. Roldan Lopez de Hierro, ω-interpolative Ciric-Reich-Rus-type contractions, Mathematics. 7 (2019), 57.
  20. A. Gupta, P. Gautam, Quasi-partial b-metric spaces and some related fixed point theorems, Fixed Point Theory Appl. 2015 (2015), 18.
  21. A. Gupta, P. Gautam, Topological structure of quasi-partial b-metric space, Int. J. Pure Math Sci. 17 (2016), 8-18.
  22. P. Gautam, V. N. Mishra, K. Negi, Common Fixed point theorems for cyclic Reich-Rus-Ciric contraction mappings in quasi-partial b-metric space, Ann. Fuzzy Math. Inf. 12(1) (2020), 47-56.
  23. P. Gautam, V. N. Mishra, R. Ali, S. Verma, Interpolative Chatterjea and cyclic Chatterjea contraction on quasi-partial b-metric space, AIMS Math. 6(2) (2021), 1727-1742.
  24. V. N. Mishra, L. M. Sanchez Ruiz., P. Gautam, S. Verma, Interpolative Reich-Rus-Ciric and Hardy-Rogers contraction on quasi-partial b-metric space and related fixed point results, Mathematics. 8 (2020), 1598.
  25. L. M. S ´anchez Ruiz., P. Gautam, S. Verma, Fixed point of interpolative Reich-Rus-Ciri ´c and contraction mapping on Rectangular quasi-partial b-metric space, Symmetry. 13(1) (2021), Art. ID 32.
  26. 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.
  27. P. Gautam, S. Verma, M. De La Sen, S. Sundriyal, Fixed point results for ω-interpolative Chatterjea type contraction in quasi-partial b-metric space, Int. J. Anal. Appl. 19 (2021), 280-287.
  28. P. Gautam, L. M. Sanchez Ruiz, S. Verma, G. Gupta, Common fixed point results on generalized weak compatible mapping in quasi-partial b-metric space, J. Math. 2021 (2021), Art. ID 5526801.
  29. P. Gautam, S. Verma, S. Gulati, omega-Interpolative Ciric-Reich-Rus type contraction on quasi-partial b-metric space, Filomat. Accepted.
  30. H. Fukhar-ud-din, V. Berinde, Iterative methods for the class of quasi-contractive type operators and comparsion of their rate of convergence in convex metric spaces, Filomat. 30(1) (2016), 223-230.