DOI QR코드

DOI QR Code

DOUBLE CONTROLLED CONE METRIC SPACES AND THE RELATED FIXED POINT THEOREMS

  • Tayebeh Lal Shateri (Department of Mathematics and Computer Sciences, Hakim Sabzevari University)
  • Received : 2021.12.28
  • Accepted : 2023.01.09
  • Published : 2023.02.28

Abstract

In this paper, we introduce double controlled cone metric spaces via two control functions. An example of a double controlled cone metric space by two incomparable functions, which is not a controlled metric space, is given. We also provide some fixed point results involving Banach type and Kannan type contractions in the setting of double controlled cone metric spaces.

Keywords

Acknowledgement

The referees have reviewed the paper very carefully. The author express their deep thanks for the comments.

References

  1. M. Abbas & B.E. Rhoades: Fixed and periodic point results in cone metric space. Appl. Math. Lett. 22 (2009), no. 4, 511-515. https://doi.org/10.1016/j.aml.2008.07.001
  2. M. Abbas & G. Jungck: Common fixed point results for noncommuting mappings without continuity in cone metric spaces. J. Math. Anal. Appl. 341 (2008), 416-420. https://doi.org/10.1016/j.jmaa.2007.09.070
  3. T. Abdeljawad, N. Mlaiki, H. Aydi & N. Souayah: Double controlled metric type spaces and some fixed point results. Mathematics. 6 (2018), Article ID 320.
  4. S. Banach: Sur les operations dans les ensembles abstraits et leur application aux quations intgrales. Fund. Math. 3 (1922), 133-181 (French). https://doi.org/10.4064/fm-3-1-133-181
  5. I.A. Bakhtin: The contraction mapping principle in almost metric spaces. Funct. Anal. 30 (1989), 26-37.
  6. I. Beg, A. Bartwal, S. Rawat, and R.C. Dimri: Best proximity points in noncommutative Banach spaces Comp. Appl. Math. 41(41) (2022). https://doi.org/10.1007/s40314-021-01741-x.
  7. H. Cakalli, A. Sonmez & C. Genc: On equivalence of topological vector Space valued cone metric spaces and metric spaces. Appl. Math. Lett. 25 (2012), 429-433. https://doi.org/10.1016/j.aml.2011.09.029
  8. N. Caki'c, Z. Kadelburg, S. Radenovi'c & A. Razani: Common fixed point results in cone metric spaces for family of weakly compatible maps Adv. Appl. Math. Sci. 1 (2009), no. 1, 183-207.
  9. K. Deimling: Nonlinear Functional Analysis Springer-Verlag, Berlin Heidelberg, 1985.
  10. L.-G. Huang & X. Zhang: Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332 (2007), no. 2, 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
  11. E. Karapinar: A new non-unique fixed point theorem Ann. Funct. Annal. 2 (2011), no. 1, 51-58. https://doi.org/10.15352/afa/1399900261
  12. Z.D. Mitrovi'c & S. Radenovi'c: The Banach and Reich contractions in bv(s)-metric spaces. J. Fixed Point Theory Appl. 19 (2017), 3087-3095. doi: 10.1007/s11784-017-0469-2.
  13. N. Mlaiki, H. Aydi, N. Souayah & T. Abdeljawad: Controlled metric type spaces and the related contraction principle. Mathematics, 6 (2018), no. 10, Article ID 194.
  14. N. Mlaiki: Double controlled metric-like spaces. J. Inequal. Appl. 2020(189) (2020).
  15. S. Rawat, S. Kukreti & R.C. Dimri: Fixed point results for enriched ordered contractions in noncommutative Banach spaces. J. Anal. 30 (2022), 1555-1566. https://doi.org/10.1007/s41478-022-00418-w.
  16. S. Reich: Kannan's fixed point thorem. Boll. Un. Math. Ital. 4 (1971), 1-11.
  17. JR. Roshan, V. Parvaneh, Z. Kadelburg & N. Hussain: New fixed point results in b-rectangular metric spaces. Nonlinear Anal.: Modelling and Control, 21 (2016), no. 5, 614-634. https://doi.org/10.15388/NA.2016.5.4
  18. D. Turkoglu & M. Abuloha: Cone metric spaces and fixed point theorems in diametrically contractive mappings. Acta Math. Sin. Engl. Series, 26 (2010), no. 3, 489-496. https://doi.org/10.1007/s10114-010-8019-5
  19. H. L-Guang & Z. Xian: Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332 (2007), 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087