New Fixed Point Theorems for θ-φ-Contraction on Quasi-Metric Spaces

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Abdelkarim Kari, Kastriot Zoto, Zamir Selko

Abstract

In this paper, we introduce the concept of θ−contraction and θ−φ−contraction in a generalized setting such as quasi-metric spaces with the aim to study existence of the unique fixed point for self mapping. Our established theorems extend and elaborate classical conclusions of standart metric supported by many examples and corollaries as a further completion of the results in the current literature.

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References

  1. S. Banach, Sur Les Opérations Dans Les Ensembles Abstraits Et Leur Application Aux éQuations Intégrales, Fundam. Math. 3 (1922), 133–181. https://doi.org/10.4064/fm-3-1-133-181.
  2. D.W. Boyd, J.S.W. Wong, On Nonlinear Contractions, Proc. Amer. Math. Soc. 20 (1969), 458–464. https://doi.org/10.2307/2035677.
  3. J. Collins, J. Zimmer, An Asymmetric Arzelà-Ascoli Theorem, Topol. Appl. 154 (2007), 2312–2322. https://doi.org/10.1016/j.topol.2007.03.006.
  4. M. Jleli, E. Karapınar, B. Samet, Further Generalizations of the Banach Contraction Principle, J. Inequal. Appl. 2014 (2014), 439. https://doi.org/10.1186/1029-242x-2014-439.
  5. R. Kannan, Some Results on Fixed Points–II, Am. Math. Mon. 76 (1969), 405–408. https://doi.org/10.2307/2316437.
  6. S. Romaguera, P. Tirado, A Characterization of Smyth Complete Quasi-metric Spaces Via Caristi’s Fixed Point Theorem, Fixed Point Theory Appl. 2015 (2015), 183. https://doi.org/10.1186/s13663-015-0431-1.
  7. S. Park, On Generalizations of the Ekeland-type Variational Principles, Nonlinear Anal.: Theory Methods Appl. 39 (2000), 881–889. https://doi.org/10.1016/s0362-546x(98)00253-3.
  8. S. Reich, Some Remarks Concerning Contraction Mappings, Can. Math. Bull. 14 (1971), 121–124. https://doi.org/10.4153/cmb-1971-024-9.
  9. H. Saffaj, K. Chaira, M. Aamri, E.M. Marhrani, A Generalization of Contraction Principle in Quasi-Metric Spaces, Bull. Math. Anal. Appl. 9 (2017), 92–108.
  10. H. Saffaj, K. Chaira, M. Aamri, E.M. Marhrani, Fixed Point Theorems for Generalized Weakly Contractive Mappings in Quasi-Metric Space, Adv. Fixed Point Theory, 7 (2017), 44–66.
  11. N. Shahzad, O. Valero, M.A. Alghamdi, M.A. Alghamdi, A Fixed Point Theorem in Partial Quasi-metric Spaces and an Application to Software Engineering, Appl. Math. Comput. 268 (2015), 1292–1301. https://doi.org/10.1016/j.amc.2015.06.074.
  12. W. Shatanawi, M.S. Md Noorani, H. Alsamir, A. Bataihah, Fixed and Common Fixed Point Theorems in Partially Ordered Quasi-Metric Spaces, J. Math. Comput. Sci. 16 (2016), 516–528. https://doi.org/10.22436/jmcs.016.04.05.
  13. D. Zheng, Z. Cai, P. Wang, New Fixed Point Theorems for θ−ϕ Contraction in Complete Metric Spaces, J. Nonlinear Sci. Appl. 10 (2017), 2662–2670. https://doi.org/10.22436/jnsa.010.05.32.
  14. W.A. Wilson, On Quasi-Metric Spaces, Amer. J. Math. 53 (1931), 675–684. https://doi.org/10.2307/2371174.