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Fuzzy fixed point results with rational type contractions in partially ordered complex-valued metric spaces

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this manuscript, some fixed point results for fuzzy mappings with rational type contraction in the context of a complete partially ordered complex-valued metric space are established. The derived results generalize some fixed point theorems in the existing literature. An appropriate example is given.
Rocznik
Strony
57--78
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
  • Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
autor
  • Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
autor
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
Bibliografia
  • [1] J. Ahmad, Ch. Klin-Eam, and A. Azam, Common fixed points for multivalued mappings in complex-valued metric spaces with applications, Abstr. Appl. Anal. (2013), 12 pages, Article ID 854965, DOI 10.1155/2013/854965.
  • [2] A. Azam, J. Ahmad, and P. Kumam, Common fixed point theorems for multi-valued mappings in complex-valued metric spaces, J. Inequal. Appl. 578 (2013), 12 pages, DOI 10.1186/1029-242x-2013-578.
  • [3] SC. Arora and V. Sharma, Fixed points for fuzzy mappings, Fuzzy Sets System 110 (2000), no. 1, 127-130, DOI 10.1016/s0165-0114(97)00366-7.
  • [4] A. Azam, B. Fisher, and M. Khan, Common fixed point theorems in complex-valued metric spaces, Numeri. Func. Anal. Appl. 32 (2011), 243-253, DOI 10.1080/01630563.2011.533046.
  • [5] L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), no. 2, 1468-1476, DOI 10.1016/j.jmaa.2005.03.087.
  • [6] A. Azam and I. Beg, Common fuzzy fixed point for fuzzy mappings, Fixed Point Theory Appl. 14 (2013), 1-11, DOI 10.1186/1687-1812-2013-14.
  • [7] S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales, Fund. Math. 3 (1922), 133-181.
  • [8] I. Beg, A. R. Bhutt, and S. Radojević, The contraction principal for the set valued mappings on metric spaces with agraph, Comput. Math. Appl. 60 (2010), no. 5, 1214-1219, DOI 10.1016/j.camwa.2010.06.003.
  • [9] I. Cabrera, J. Harjani, and K. Sadarangani, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara. 59 (2013), no. 2, 251-258, DOI 10.1007/s11565-013-0176-x.
  • [10] Lj. B. Ćirić, A generalization of Banach contraction principal, Proc. Amer. Math. Soc. 45 (1974), no. 2, 267-273, DOI 10.2307/2039386.
  • [11] V. D. Estruch and A. Vidal, A note on fixed point for fuzzy mappings, Rend. Istit. Math. Univ. Trieste 32 (2001), 39-45.
  • [12] T. Dosenović, D. Rakić, B. Carić, and S. Radenović, Multivalued generalizations of fixed point results in fuzzy metric spaces, Nonlinear Anal. Model. Control 2 (2015), 211-222, DOI 10.15388/NA.2016.2.5.
  • [13] A. Green and J. Pastor, A fixed point theorem for fuzzy contraction mapping, Rend. Instit. Math. Univ. Trieste 30 (1999), 103-109.
  • [14] S. Heilpern, Fuzzy fixed point theorems, J. Math. Anal 83 (1981), 566-569.
  • [15] A. Hojat, O. Ege, and S. Radenović, Some fixed point theorem in complex-valued Gb metric space, Rev. Acad. Cience. Exact. Fis. Natur. (2017), 1579-1505.
  • [16] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 6 (1968), 71-78.
  • [17] E. Karapinar and R. Agarwal, Further fixed point results on G-metric space, Fixed Point Theory Appl. 154 (2013), no. 6, 1-14, DOI 10.1186/1687-1812-2013-154.
  • [18] C. Klin-Eam and C. Suanoom, Some common fixed point theorems for generalized contractive type mappings on complex-valued metric spaces, Abstr. Appl. Anal. 6 (2013), 1-6, DOI 10.1155/2013/604215.
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  • [20] S. Radenović, Common fixed points under contractive conditions in cone metric spaces, Comput. Math. Appl. 58 (2009), no. 6, 1273-1278, DOI 10.1016/j.camwa.2009.07.035.
  • [21] S. Radenović and B. E. Rhoades, Fixed point theorems for two non self mappings in cone metric spaces, Comput. Math. Appl. 57 (2009), no. 10, 1701-1707, DOI 10.1016/j.camwa.2009.03.058.
  • [22] S. Radenović, P. Salimi, C. Vetro, and T. Dosenović, Edelstein Suzuki-type results for self-mappings in various abstract spaces with application to functional equations, Acta Math. Appl. Sin. 36 (2016), no. 1, 94-110, DOI 10.1016/s0252-9602(15)30081-3.
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  • [25] B. S. Choudhury, N. Metiya, and P. Konar, Fixed point results for rational type contraction in partially ordered complex-valued metric spaces, Bull. Int. Math. Virtual. Inst. 5 (2015), 73-80.
  • [26] M. S. Abdullahi and A. Azam, Multi-valued fixed points results viarational type contractive conditions in complex-valued metric spaces, J. Int. Math. Virtual Inst. 7 (2017), no. 8, 119-146.
  • [27] W. Shatanawi, V. C. Rajic, S. Radenović, and A. Al-Ravashedeh, Mizoguchi-Takahashi-type theorem in tvs cone metric spaces, Fixed Point Theory Appl. 106 (2012), no. 1, DOI 10.1186/1687-1812-2012-106.
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  • [29] Y. Tiana and Z. Bai, Existence results for the three-point impulsive boundary value problem involving fractional differential equations, Comput. Math. Appl. 59 (2010), 2601-2609, DOI 10.1016/j.camwa.2010.01.028.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a84ef963-b72d-44ee-a3e2-01911e397fee
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