Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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COMMON FIXED POINT RESULTS FOR MAPPINGS UNDER NONLINEAR CONTRACTION OF CYCLIC FORM IN b-METRIC SPACES

  • Rabaiah, Ayat (Department of Mathematics, Faculty of Science The University of Jordan) ;
  • Tallafha, Abdallah (Department of Mathematics, Faculty of Science The University of Jordan) ;
  • Shatanawi, Wasfi (Department of Mathematics, Faculty of General Science Prince Sultan University, Department of Mathematics, Faculty of Science Hashemite University)
  • Received : 2020.09.06
  • Accepted : 2021.02.05
  • Published : 2021.06.15
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Abstract

In this research, we interpret the notion of a b-cyclic (𝚽, C, D)-contraction for the pair (g, S) of self-mappings on the set Y. We employ our definition to introduce some common fixed point theorems for the two mappings g and S under a set of conditions. Also we introduce an example to support our results.

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References

  1. M. Abbas, W. Shatanawi, S. Farooq and Z.D. Mitrovic, On a JH-operators pair of type (A) with applications to integral equations, J. Fixed Point Theory Appl., 22 (2020), Article number 72.
  2. K. Abodayeh, T. Qawasmeh, W. Shatanawi and A. Tallafha, Eφ-contraction and some fixed point results via modified -distance mappings in the frame of complete quasi metric spaces and applications, Inter. J. Elect. Comput. Eng., 10 (2020), 3839-3853. https://doi.org/10.11591/ijece.v10i4.pp3839-3853
  3. E. Ameer, H. Aydi, H.A. Hammad, W. Shatanawi and N. Mlaiki, On (φ, ψ)-metric spaces with applications, Symmetry, 12 (2020), Article number 1459.
  4. H.Aydi, E. Karapinar and W. Shatanawi, Coupled fixed point results for (ψ, φ)-weakly contractive contractive condition in ordered partial metric space, Comput. Math. Appl., 62 (2011), 4449-4460. https://doi.org/10.1016/j.camwa.2011.10.021
  5. H. Aydi, W. Shatanawi, M, Postolache, Z. Mustafa and N. Tahat, Theorems for Boyd-Wong-type contractions in ordered metric spaces, Abstr. Appl. Anal., 2012 (2012), Article number 359054.
  6. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., 30 (1989), 26-37.
  7. A. Bataihah, W. Shatanawi, T. Qawasmeh and R. Hatamleh, On H-Simulation functions and fixed point results in the setting of wt-distance mappings with application on matrix equations, Mathematics, 8 (2020), Article number 837.
  8. A. Bataihah, W. Shatanawi and A. Tallafha, Fixed point results with simulation functions, Nonlinear Funct. Anal. Appl., 25 (2020), 13-23.
  9. A. Bataihah, A. Tallafha and W. Shatanawi, Fixed point results with Ω-distance by utilizing simulation functions, Italian J. Pure and Appl. Math., 43 (2020), 185-196.
  10. Y.J. Cho, B.E. Rhoades, R. Saadait, B. Samet and W. Shatanawi Nonlinear coupled fixed point theorems in ordered generalized metric space with integral type, Fixed Point Theory Appl., 2012. Article ID (2012)
  11. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univa. Ostra., 1 (1993), 5-11.
  12. S. Czerwik, Nonlinear set-valued contraction mappings in b-metric space, Atti Sem. Mat. Uniu. Modena, 46 (1998), 263-276.
  13. U. Kadak, On the classical sets of sequences with fuzzy b-metric, Gen. Math. Notes. 23(1) (2014), 89-108.
  14. N. Kir and H. Kiziltun, On some well Know fixed point theorems in b-metric space, Turk. J. Anal. Number Theory, 1 (2013), 13-16.
  15. W.A. Kirk, S.P. Srinavasan and P. Veeramanyi, Fixed points for mapping satisfying cyclical conditions, Fixed Point Theory Appl., 4 (2003), 79-89.
  16. A. Khan, T. Abdeljawad, W. Shatanawi and H. Khan, Fixed point theorems for Quadruple self-mappings satisfying integral type inequalities, Filoma, 34(3) (2020), 905-917, https://doi.org/10.2298/FIL2003905K
  17. M.S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30 (1984), 1-9. https://doi.org/10.1017/S0004972700001659
  18. K. Kukic, W. Shatanawi and M.G. Filipovic, Khan and Ciric contraction princples in almost b-metric space, U.P.B. Sci. Bull., Series A, 82, Iss. 1, (2020).
  19. A. Mukheimer, N. Mlaiki, K. Abodayeh and W.Shatanawi, New theorems on extended b-metric spaces under new contractions, Nonlinear Anal, Model. Con., 24(6) (2019), 870-883.
  20. M. Pcurar and I.A. Rus, Fixed point theory for cyclic φ-contractions, Nonlinear Anal., 72 (2010), 1181-1187. https://doi.org/10.1016/j.na.2009.08.002
  21. G. Petruel, Cyclic representations and periodic points, Stud. Univ. Babe-Bolyai, Math., 50 (2005), 107-112.
  22. H. Qawaqneh, M.S.M. Noorani and W. Shatanawi, Fixed point theorems for (α, k, θ)-contractive multi-valued mapping in b-metric space and applications, Int. J. Math. Comput. Sci., 14(1) (2019), 263-283.
  23. H. Qawaqneh, M.S.M. Noorani, S. Shatanawi, H. Aydi and H. Alsamir, Fixed point results for multi-valued contractions in b-metric spaces and an application, Mathematics, 7 (2019), Article number 132.
  24. T. Qawasmeh, A. Tallafha and W. Shatanawi, Fixed and common fixed point theorems through modified ω-distance mappings, Nonlinear Funct. Anal. Appl., 24 (2019), 221-239.
  25. T. Qawasmeh, A. Tallafha and W. Shatanawi, Fixed point theorems through modified w-distance and application to nontrivial equations, Axioms, 8 (2019), Article Number 57.
  26. K.P.R. Rao, W. Shatanawi, G.N.V. Kishore, K. Abodayeh and D.R. Prasad, Existeness and uniqeness of Suzuki type results in S bmetric spaces with applications to integral equations, Nonlinear Funct. Anal. Appl., 23 (2018), 225-245. https://doi.org/10.22771/NFAA.2018.23.02.02
  27. J.R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei and W. Shatanawi, Common fixed points of almost generalized (ψ, φ)s-contractive mappings in ordered bmetric spaces, Fixed Point Theory Appl., 2013:159 (2013).
  28. S. Sedghi, N. Shobkolaei, J. Rezaei Roshan and W. Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Matematicki Vesnik, 66(2) (2014), 190-201.
  29. W. Shatnawi and Postolache Mihai, Common fixed point results for mappings under nonlinear contraction of cyclic form in ordered metric spaces, A springer open journal, (2013).
  30. W. Shatanawi, and S. Manro, Fixed point results for cyclic (ψ, φ, A, B)-contraction in partial metric space, Fixed point Theory Appl., 2012 (2012). Article ID. 165.
  31. W. Shatanawi and B. Samet, On (ψ, φ)-weakly contractive condition in partially ordered metric space, Comput. Math. Appl., 62 (2011), 3204-3214. https://doi.org/10.1016/j.camwa.2011.08.033
  32. W. Shatanawi, Some coincidence point result in cone metric space, Math. Comput .Modle., 55 (2012), 2023-2028. https://doi.org/10.1016/j.mcm.2011.11.061
  33. W. Shatanawi, Some fixed point theorems in ordered G-metric space and applications, Abstr. Appl. Anal., 2011 (2011), Article ID 126205.
  34. W. Shatanawi, On w-compatible mappings and common coupled coincidence point in cone metric spaces, Appl. Math. Lett., 25 (2012), 925-931. https://doi.org/10.1016/j.aml.2011.10.037
  35. W. Shatanawi, Some fixed point results for a generalized ψ-weak contraction mappings in orbitally metric spaces, Chaos, Solitons and Fractals, 45 (2012), 520-526. https://doi.org/10.1016/j.chaos.2012.01.015
  36. W. Shatanawi, A. Bataihah and A. Tallafha, Four-step iteration scheme to approximate fixed point for weak contractions, Comput. Materials Continua CMC, 64 (2020), 1491-1504. https://doi.org/10.32604/cmc.2020.010365
  37. W. Shatanawi, E. Karapnar and H. Aydi, Coupled coincidence points in partially ordered cone metric spaces with a c-distance, J. Appl. Math., 2012 (2012), Article number 312078.
  38. W. Shatanawi, Z. Mustafa and N. Tahat, Some coincidence point theorems for nonlinear contraction in ordered metric spaces, Fixed Point Theory Appl., 2011 (2011), Article number 68.
  39. W. Shatanawi and A. Pitea, Fixed and coupled fixed point theorems of Ω-distance for nonlinear contraction, Fixed Point Theory Appl., 2013(11) (2013), DOI: 10.1186/1687-1812-2013-275.
  40. W. Shatanawi, A. Pitea and R. Lazovi, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory Appl., 2013:120 (2013). https://doi.org/10.1186/1687-1812-2013-120
  41. W. Shatanawi and M. Postolache, Common fixed point theorems for dominating and weak annihilator mappings in ordered metric spaces, Fixed Point Theory Appl., 2013 (2013), Article number 271.
  42. W. Shatanawi, V.C. Rajic, S.C. Radenovic and A. Al-Rawashdeh, Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces, Fixed Point Theory Appl., 2012 (2012), Article number 106.