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A Suzuki type unique common fixed point theorem for two pairs of hybrid maps under a new condition in partial metric spaces

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce a new condition namely: condition (W.C.C.) and utilize the same to prove a Suzuki type unique common fixed point theorem for two hybrid pairs of mappings in partial metric spaces employing the partial Hausdorff metric which generalizes several known results of the existing literature proved in metric and partial metric spaces.
Wydawca
Rocznik
Strony
79--94
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • Department of Mathematics Acharya Nagarjuna University Nagarjuna Nagar-522 510, A.P., India
autor
  • Department of Mathematics Gitam University Rudraram(V), Patancheru(M), Hyderabad-502 329, T.P., India
autor
  • Department of Mathematics Aligarh Muslim University Aligarh-202 002 , U.P., India
Bibliografia
  • [1] H. Aydi, M. Abbas, C. Vetro, Partial Hausdrouff metric and Nadler’s fixed point theorem on partial metric space, Topology Appl. 159(14) (2012), 3234–3242.
  • [2] B. Damjanovic, B. Samet, C. Vetro, Common fixed point theorems for multi-valued maps, Acta Math. Sci. Ser. B (English Ed.) 32 (2012), 818–824.
  • [3] D. Paesano, P. Vetro, Suzuki’s type characterization of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl. 159(3) (2012), 911–920.
  • [4] K. P. R. Rao, G. N. V. Kishore, K. A. S. N. V. Prasad, A unique common fixed point theorem for two maps under (Ψ – Φ) contractive condition in partial metric spaces, Mathematical Sciences, (Springer open Journal) 6:9(2012 ), doi:10.1186/2251-7456-6-9.
  • [5] Lj. Ciric, B. Samet, H. Aydi, C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), 2398–2406.
  • [6] C. Di Bari, P. Vetro, Fixed points for weak φ contractions on partial metric spaces, Int. J. Eng. Contemp. Math. Sci. 1(1) (2011), 5–13.
  • [7] K. P. R. Rao, G. N. V. Kishore, A unique common fixed point theorem for four maps under (Ψ – Φ) contractive condition in partial metric spaces, Bulletin of Mathematical Analysis and Applications 3(3) (2011), 56–63.
  • [8] I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. 157 (2010), 2778–2785.
  • [9] B. D. Rouhani, S. Moradi, Common fixed point of multivalued generalized φ weak contractive mappings, Fixed Point Theory and Applications vol. 2010, Article ID708984, 13 pages.
  • [10] I. Altun, H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud. 1 (2008), 1–8.
  • [11] P. Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl. 192(2) (1995), 655–666.
  • [12] S. G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., Vol. 728, 1994, pp. 183–197.
  • [13] S. B. Nadler, Mutivalued contraction mappings, Pacific. J. Math. 30 (1969), 475–488.
  • [14] M. Kikkawa, T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008), 2942–2949.
  • [15] D. Djoric, R. Lazovic, Some Suzuki type fixed point theorems for generalized multi-valued mappings and applications, Fixed Point Theory Appl. 2011, 2011:40, doi:10.11861687-1812-2011-40.
  • [16] S. L. Singh, S. N. Mishra, R. Chugh, R. Kamal, General common fixed point theorems and applications, J. Applied Mathematics, Vol. 2012, Artical ID 902312, 14 pages.
  • [17] Lj. Ciric, Multi-valued nonlinear contraction mappings, Nonlinear Anal. 71 (2009), 2716–2723.
  • [18] C. Di Bari, Z. Kadelburg, H. K. Nashine, S. Radenovic, Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces, Fixed Point Theory Appl. 2012, 2012:113.
  • [19] C. Di Bari, M. Milojevic, S. Radenovic, P. Vetro, Common fixed points for self-mappings on partial metric spaces, Fixed Point Theory Appl. 2012, 2012:140.
  • [20] R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Categ. Structures 7 (1999), 71–83.
  • [21] S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl. 2010, 2010:493298, 6 pages.
  • [22] S. Romaguera, O. Valero, A quantitative computational model for complete partial metric spaces via formal balls, Math. Structures Comput. Sci. 19 (2009), 541–563.
  • [23] M. P. Schellekens, The correspondence between partial metrics and semivaluations, Theoret. Comput. Sci. 315 (2004), 135–149.
  • [24] F. Vetro, S. Radenovic, Nonlinear φ-quasi-contractions of Ciric-type in partial metric spaces, Appl. Math. Comput. 219 (2012), 1594–1600.
  • [25] M. Abbas, B. Ali, C. Vetro, A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces, Topology Appl. 160 (2013),553–563.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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