Well-posedness and porosity of a certain class of operators

• Autorzy: Lahiri B. , Das P.
• Języki publikacji: EN

Abstrakty

EN

We prove that several fixed point problems are well-posed and study the porosity behaviour of a certain class of operators.

Słowa kluczowe

EN

operators; fixed point problem; well-posedness; T-orbitally complete; quasi-contractive; uniformly very porous

PL

operatory; problem punktu stałego; klasy operatorów

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 169--176
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Lahiri B.

• B-1/146 Kalyani, West Bengal - 741235, India

autor

Das P.

• Department of Mathematics, Jadavpur University, Kolkata - 32, West Bengal, India

Bibliografia

• [1] Lj. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45 (2) (1974), 267-273.
• [2] F. S. De Blasi and J. Myjak, Sur la porosite des contractions sans point fixe, C. R. Acad. Sci. Paris, 308 (1989), 51-54.
• [3] B. Fisher, Quasi-contractions on metric spaces, Proc. Amer. Math. Soc. 75 (2) (1979), 321-325.
• [4] R. Kannan, Some results on fixed points - II, Amer. Math. Monthly 76 (45) (1969), 405-408.
• [5] R. P. Pant, Discontinuity and fixed points, J. Math. Anal. and Appl. 240 (1999), 284-289.
• [6] E. Rakotch, A note on contractive mappings, Proc. Amer. Math. Soc. 13 (1962), 459-465.
• [7] S. Reich and A. J. Zaslavski, Almost all non-expansive mappings are contractive, C. R. Math. Rep. Acad. Sci. Canada 22 (3) (2000), 118-124.
• [8] S. Reich and A. J. Zaslavski, The set of non-contractive mappings is σ-porous in the space of all non-expansive mappings, C. R. Acad. Sci. Paris 333 (2001), 539-544.
• [9] S. Reich and A. J. Zaslavski, Well-posedness of fixed point problems, Far East J. Math. Sci., special volume (2001), Part III, 393-401.
• [10] T. Śalát, S. J. Taylor and J. T. Tóth, Radii of convergence of power series, Real Anal. Exchange, 24 (1) (1998-99), 263-274.
• [11] J. Tkadlec, Constructions of some non-σ-porous sets of real line, Real Anal. Exchange, 9 (1983-84), 473-482.
• [12] L. Zajićek, Sets of σ-porosity and sets of σ-porosity (q), Cas. Pest. Mat. 101 (1976), 350-359.
• [13] L. Zajićek, Porosity and σ-porosity, Real Anal. Exchange 13 (1987-88), 314-350.