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2 results

  • ON CONNECTIONS BETWEEN DELTA-CONVEX MAPPINGS AND CONVEX OPERATORS

  • Libor Veselý, Luděk Zajíček
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 3 / October 2006
    Published online by Cambridge University Press:
    25 January 2007, pp. 739-751
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  • We study conditions under which every delta-convex (d.c.) mapping is the difference of two continuous convex operators, and vice versa. In particular, we prove that each d.c. mapping $F:(a,b)\to Y$ is the difference of two continuous convex operators whenever $Y$ belongs to a large class of Banach lattices which includes all $L^{p}(\mu)$ spaces ($1\leq p\leq\infty$). The proof is based on a result about Jordan decomposition of vector-valued functions. New observations on Jordan decomposition of finitely additive vector-valued measures are also presented.

  • 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.