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2 results

  • A NEW EXTENSION OF DARBO’S FIXED POINT THEOREM USING RELATIVELY MEIR–KEELER CONDENSING OPERATORS

  • Part of
  • MOOSA GABELEH, CALOGERO VETRO
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 98 / Issue 2 / October 2018
    Published online by Cambridge University Press:
    19 July 2018, pp. 286-297
    Print publication:
    October 2018
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  • We consider relatively Meir–Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. [‘Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness’, Acta Math. Sci. Ser. B35 (2015), 552–566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations.

  • On Fixed Points of Asymptotically Regular Mappings

  • Part of
  • B. E. Rhoades, S. sessa, M. S. Khan, M. Swaleh
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 43 / Issue 3 / December 1987
    Published online by Cambridge University Press:
    09 April 2009, pp. 328-346
    Print publication:
    December 1987
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  • Some results on fixed points of asymptotically regular mappings are obtained in complete metric spaces and normed linear spaces.

    The structure of the set of common fixed points is also discussed in Banach spaces. Our work generalizes essentially known results of Das and Naik, Fisher, Jaggi, Jungck, Rhoades, Singh and Tiwari and several others.