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2006 | 26 | 1 | 5-55
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Some algebraic fixed point theorems for multi-valued mappings with applications

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EN
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EN
In this paper, some algebraic fixed point theorems for multi-valued discontinuous operators on ordered spaces are proved. These theorems improve the earlier fixed point theorems of Dhage (1988, 1991) Dhage and Regan (2002) and Heikkilä and Hu (1993) under weaker conditions. The main fixed point theorems are applied to the first order discontinuous differential inclusions for proving the existence of the solutions under certain monotonicity condition of multi-functions.
Twórcy
  • Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India
Bibliografia
  • [1] R.P. Agarwal, B.C. Dhage and D. O'Regan, The method of upper and lower solution for differential inclusions via a lattice fixed point theorem, Dynamic Systems & Appl. 12 (2003), 1-7.
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  • [9] B.C. Dhage, A lattice fixed point theorem for multi-valued mappings and applications, Chinese Journal of Math. 19 (1991), 11-22.
  • [10] B.C. Dhage, Some fixed point theorems in ordered Banach spaces and applications, The Math. Student 63 (1-4) (1992), 81-88.
  • [11] B.C. Dhage, Fixed point theorems in ordered Banach algebras and applications, PanAmer. Math. J. 9 (4) (1999), 93-102.
  • [12] B.C. Dhage, A functional integral inclusion involving Carathéodories, Electronic J. Qualitative Theory Diff. Equ. 14 (2003), 1-18.
  • [13] B.C. Dhage, A functional integral inclusion involving discontinuities, Fixed Point Theory 5 (2004), 53-64.
  • [14] B.C. Dhage, Multi-valued operators and fixed point theorems in Banach algebras I, Taiwanese J. Math. 10 (2006), 1025-1045.
  • [15] B.C. Dhage, A fixed point theorem in Banach algebras involving three operators with applications, Kyungpook Math. J. 44 (2004), 145-155.
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  • [17] B.C. Dhage, A fixed point theorem for multi-valued mappings in ordered Banach spaces with applications I, Nonlinear Anal. Forum 10 (2005), 105-126.
  • [18] B.C. Dhage and D. O'Regan, A lattice fixed point theorem and multi-valued differential equations, Functional Diff. Equations 9 (2002), 109-115.
  • [19] B.C. Dhage and S.M. Kang, Upper and lower solutions method for first order discontinuous differential inclusions, Math. Sci. Res. J. 6 (11) (2002), 527-533.
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  • [23] S. Heikkilä, On chain method used in fixed point theory, Nonlinear Studies 6 (2) (1999), 171-180.
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Bibliografia
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