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Tytuł artykułu

Two generalized common fixed point theorems involving compatibility and property E.A.

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove two generalizations: the first to Das and Naik’s theorem for a pair of compatible maps without continuity; and the next as an extension of our first result to three self-maps on a metric space X without compatibility, under a stronger contraction type inequality and restricting the completeness of X to its subspace. The latter is a significant generalization of a recent result of Pant et al.
Wydawca
Rocznik
Strony
449--458
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
  • Applied Analysis Division, School of Advanced Sciences Vit University, Vellore-632014,Tamil Nadu, India
  • Nalla Malla Reddy Engineering College, Rr District Hyderabad-500088(Ap), India
Bibliografia
  • [1] M. A. Aamri, D. El. Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), 181–188.
  • [2] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29(9) (2002), 531–536.
  • [3] Lj. B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974), 271–273.
  • [4] P. Collaco, J. C. E. Silva, A complete comparison of 25 contractive conditions, Nonlinear Anal. 30(1) (1997), 471–476.
  • [5] J. Danes, Two fixed point theorems in topological and metric spaces, Bull. Austral. Math. Soc. 14 (1976), 259–265.
  • [6] K. M. Das, V. Naik, Common fixed point theorems for commuting maps on metric space, Proc. Amer. Math. Soc. 83 (1981), 645–652.
  • [7] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261–263.
  • [8] G. Jungck, Compatible maps and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771–779.
  • [9] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71–76.
  • [10] J. Kinces, V. Totok, Theorems and counterexamples on contractive mappings, Math. Balkanica (N.S.) 4(1) (1990), 69–90.
  • [11] I. H. N. Rao, K. P. R. Rao, Unique common fixed point of pair of non linear mappings, Pure Appl. Math. Sci. 17 (1983), 63–66.
  • [12] R. P. Pant, A common fixed point theorem under a new condition, Indian J. Pure Appl. Math. 30(2) (1999), 147–152. CMP 1 681 592.
  • [13] R. P. Pant, R. K. Bist, D. Arora, Weak reciprocal continuity and fixed point theorems, Ann Univ. Ferrara. 57 (2011), 181–190.
  • [14] H. K. Pathak, R. R. Lopez, R. K. Verma, A common fixed point theorem using implicit relation and property E.A. in metric spaces, Filomat 1(2) (2007), 211–234.
  • [15] T. Phaneendra, V. S. R. Prasad, A note on a claim of Rao and Rao for a pair of commuting self-maps, SAX 1(2) (2010), 81–83.
  • [16] B. E. Rhoades, A comparison of various definitions of contractive type mappings, Trans. Amer. Math. Soc. 226 (1977), 257–290.
  • [17] B. E. Rhoades, Contractive Definitions, Nonlinear Analysis, World Scientific Publishing, Singapore, 1987, 513–526.
  • [18] S. Sessa, On a weak commutativity condition in fixed point considerations, Publ. Inst. Math. 32 (1982), 149–153.
  • [19] S. L. Singh, A. Tomar, Weaker forms of commuting maps and existence of fixed points, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 10(3) (2003), 145–161.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-290abc4c-156a-44f8-b434-fc22cc8411c7
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