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Fixed point theorems in controlled rectangular metric spaces

Mohamed Rossafi|Abdelkarim Kari
한국수학교육학회|2023.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제30권 제2호|pp. 169-190|DOI https://doi.org/10.7468/jksmeb.2023.30.2.169

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키워드

fixed pointcontrolled metric type spaceextended rectangular b-metric space.
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초록

In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality in the definition of a metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.

Abstract

In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality in the definition of a metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.

참고문헌 (24)

  1. Saeed Anwar, "Existence fixed-point theorems in the partial $ b $-metric spaces and an application to the boundary value problem", AIMS Mathematics, 7(5), pp.8188~8205 (2022), American Institute of Mathematical Sciences (AIMS)[DOI]
  2. M. Asim, "Fixed point results in extended rectangular b-metric spaces with an application", UPB Sci. Bull. Ser. A, 81, pp.11~20 (2019)
  3. I. A. Bakhtin, "The contraction mapping principle in quasimetric spaces", Funct. Anal., Unianowsk Gos. Ped. Inst, 30, pp.26~37 (1989)
  4. S. Banach, "Sur les operations dans les ensembles abstraits et leur application aux equations integrales", Fund. Math, 3, pp.133~181 (1922)
  5. A. Branciari, "A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces", Publ. Math. Debrecen, 57, pp.31~37 (2000)
  6. S. Czerwik, "Contraction mappings in b-metric spaces", Acta Math. Inform. Univ. Os-traviensis, 1, pp.5~11 (1993)
  7. Muhammad Farhan, "Reich-Type and (α, F)-Contractions in Partially Ordered Double-Controlled Metric-Type Spaces with Applications to Non-Linear Fractional Differential Equations and Monotonic Iterative Method", Axioms, 11(10), pp.573~ (2022), MDPI AG[DOI]
  8. B. Fisher, "Mappings satisfying a rational inequality", Bull. Math. Soc. Sci. Math. R. S. Roumanie(N. S. ), 24, pp.247~251 (1980)
  9. R. George, "Rectangular b-metric space and contraction principles", Journal of Nonlinear Sciences and Applications, 08(06), pp.1005~1013 (2015), International Scientific Research Publications MY SDN. BHD.[DOI]
  10. R. Kannan, "Some results on fixed points-II", Amer. Math. Monthly, 76, pp.405~408 (1969)
  11. Abdelkarim Kari, "Fixed point theorem for Nonlinear F¡contraction via w¡distance", Advances in Mathematical Physics, 2020, pp.1~10 (2020), Hindawi Limited[DOI]
  12. Abdelkarim Kari, "Fixed point theorems for 𝜃-ϕ-contraction in generalized asymmetric metric spaces", International Journal of Mathematics and Mathematical Sciences, 2020, pp.1~19 (2020), Hindawi Limited[DOI]
  13. Abdelkarim Kari, "New fixed point theorems for 𝜃-ϕ-contraction on rectangular b-metric spaces", Abstract and Applied Analysis, 2020, pp.1~12 (2020), Hindawi Limited[DOI]
  14. Abdelkarim Kari, "𝜃-ϕ-contraction on (α, η)-complete rectangular b¡metric spaces", International Journal of Mathematics and Mathematical Sciences, 2020, pp.1~9 (2020), Hindawi Limited[DOI]
  15. William A Kirk, "Generalized metrics and Caristi’s theorem", Fixed Point Theory and Applications, 2013(1) (2013), Springer Science and Business Media LLC[DOI]
  16. Nabil Mlaiki, "Some New Observations on Geraghty and Ćirić Type Results in b-Metric Spaces", Mathematics, 7(7), pp.643~ (2019), MDPI AG[DOI]
  17. Muhammad Nazam, "Common Fixed-Point Theorems in the Partial b-Metric Spaces and an Application to the System of Boundary Value Problems", Journal of Function Spaces, 2021, pp.1~11 (2021), Hindawi Limited[DOI]
  18. Stojan Radenović, "A note on the paper: “Nonlinear integral equations with new admissibility types in b-metric spaces”", Journal of Fixed Point Theory and Applications, 19(4), pp.2287~2295 (2017), Springer Science and Business Media LLC[DOI]
  19. Maliha Rashid, "q-ROF mappings and Suzuki type common fixed point results in b-metric spaces with application", Journal of Inequalities and Applications, 2022(1) (2022), Springer Science and Business Media LLC[DOI]
  20. S. Reich, "Some remarks concerning contraction mappings", Canad. Math. Bull, 14(2), pp.121~124 (1971)
  21. M. Rossafi, "New fixed point theorems for θ - ϕ -contraction on b -metric spaces", Journal of Mathematics and Computer Science, 29(01), pp.12~27 (2022), International Scientific Research Publications MY SDN. BHD.[DOI]
  22. Mohamed Rossafi, "Best Proximity Point Theorems For Cyclic 𝜃-ϕ-contraction on metric spaces", 한국수학교육학회지시리즈B:순수및응용수학, 29(4), pp.335~352 (2022), 한국수학교육학회[DOI]
  23. Mohamed Rossafi, "Fixed Point Theorems For (ϕ, F)¡Contraction in Generalized Asymmetric Metric Spaces", 한국수학교육학회지시리즈B:순수및응용수학, 29(4), pp.369~399 (2022), 한국수학교육학회[DOI]
  24. Jamal Rezaei Roshan, "New fixed point results in b-rectangular metric spaces", Nonlinear Analysis: Modelling and Control, 21(5), pp.614~634 (2016), Vilnius University Press[DOI]

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