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A Common Fixed Point Theorem for Set-valued Contraction Mappings in Menger Space

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to prove a common fixed point theorem for even number of single-valued and two set-valued mappings in complete Menger space using implicit relation. Our result improves and extends the result of Chen and Chang [Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006, Art. ID 75931, 15 pp].
Rocznik
Strony
61--71
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
autor
autor
  • Near Nehru Training Centre, H. No. 274, Nai BASTI B-14, Bunor-246701, Uttar Pradesh, India, sun.gkv@gmall. com
Bibliografia
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  • [2] S. S. Chang, Y. J. Cho and S. M. Kang, Probabilistic Metric Spaces and Nonlinear Operator Theory, Sichuan Univ. Press (Chengdu) 1994.
  • [3] S. S. Chang, Y. J. Cho and S. M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Inc., New York 2001. ISBN: 1-56072 MR2018691 (2004j:47143)
  • [4] S. S. Chang, Y. J. Cho, S. M. Kang and J. X. Fan, Common fixed point theorems for multivalued mappings in Menger PM-spaces, Math. Japonica 40 (2) (1994), 289-293. MR1297244
  • [5] S. Chauhan and B. D. Pant, Common fixed point theorems for occasionally weakly compatible mappings using implicit relation, J. Indian Math. Soc. 77 (1-4) (2010), 13-21. MR2724019
  • [6] C. M. Chen and T. H. Chang, Common fixed point theorems in Menger spaces, Int. J. Math. & Math. Sci. 2006, Art. ID 75931, 15 pp. MR2251697 (2007i:47070) DOI: 10.1155/IJMMS/2006/75931
  • [7] S. Chuan, Caristi type hybrid fixed point theorems in Menger probabilistic metric space, Appl. Math. Mech. (English Ed.) 18 (2) (1997), 201-209. MR1446334 (97k:54035)
  • [8] O. Hadżić, Fixed point theorems for multivalued mappings in probabilistic metric spaces, Fuzzy Sets and Systems 88 (2) (1997), 219-226. MR1452205
  • [9] O. Hadżić and E. Pap, Probabilistic multi-valued contractions and decomposable measures, Operations for uncertainty modelling (Liptovsky Mikulas, 2002). Internat. J. Uncertain. Fuz-ziness Knowledge-Based Systems 10 (2002) (Suppl.), 59-74. MR1962669 (2004b:54070)
  • [10] O. Hadżić and E. Pap, A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Sets and Systems 127 (3) (2002), 333-344. MR1899066 (2003a:54043)
  • [11] M. Imdad and J. Ali, A general fixed point theorem in fuzzy metric spaces via an implicit function, J. Appl. Math. Inform. 26 (3-4) (2008), 591-603.
  • [12] G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (3) (1998), 227-238. MR1617919
  • [13] S. Kumar and B. D. Pant, A common fixed point theorem in probabilistic metric space using implicit relation, Filomat 22 (2) (2008), 43-52. MR2484193
  • [14] S. Kumar and B. D. Pant, Common fixed point theorems in probabilistic metric spaces using implicit relation and property (B.A), Bull. Allahabad Math. Soc. 25 (2) (2010), 223-235. MR2779240
  • [15] K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U. S. A. 28 (1942), 535-537. MR0007576 (4,163e)
  • [16] D. Mihet, A generalization of a contraction principle in probabilistic metric spaces Part II, Int. J. Math. & Math. Sci. 2005 (5), 729-736. MR2173690 (2006h:47097)
  • [17] S. N. Mishra, Common fixed points of compatible mappings in PM-spaces, Math. Japon. 36 (2) (1991), 283-289. MR1095742
  • [18] D. O'Regan and R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput. 195 (1) (2008), 86-93. MR2379198
  • [19] B. D. Pant and S. Chauhan, Common fixed point theorems for semicompatible mappings using implicit relation, Int. J. Math. Anal. (Ruse) 3 (28) (2009), 1389-1398. MR2604831
  • [20] B. D. Pant and S. Chauhan, Common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces and application, Bull. Allahabad Math. Soc. 26 (2) (2011), 285-306.
  • [21] H. K. Pathak, Y. J. Cho, S. S. Chang and S. M. Kang, Coincidence point theorems for multivalued and single-valued mappings in Menger PM-spaces, Tamkang J. Math. 26 (4) (1995), 313-319. MR1378175 (96j:54044)
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  • [23] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334. MR0115153 (22 #5955)
  • [24] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing Co., New York 1983. ISBN: 0-444-00666-4 MR0790314 (86g:54045)
  • [25] V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric spaces, Math. Systems Theory (1972), 97-102. MR0310858 (46 #9956)
  • [26] B. Singh and S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. 301 (2) (2005), 439-448. MR2105684
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0023-0063
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