Título inglés |
Contractions on probabilistic metric spaces: examples and counterexamples. |
Título español |
Contracciones en espacios métricos probabilísticos: ejemplos y contraejemplos. |
Autor/es |
Schweizer, Berthold ; Sherwood, Howard ; Tardiff, Robert M. |
Organización |
Dep. Math. State Univ. Massachusetts-Amherst, Amherst (Mass.), Estados Unidos;Dep. Math. Univ. Cent. Florida, Orlando, Estados Unidos;Dep. Math. Sci. Salisbury State Univ., Salisbury (Maryland), Estados Unidos |
Revista |
0210-7821 |
Publicación |
1988, 12 (1): 5-17, 7 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
The notion of a contraction mapping for a probabilistic metric space recently introduced by T. L. Hicks is compared with the notion previously introduced by V. L. Sehgal and A. T. Bharucha-Reid. By means of appropriate examples, it is shown that these two notions are independent. It is further shown that every Hick's contraction on a PM space (S,F,tW) is an ordinary metric contraction with respect to a naturally defined metric on that space; and it is again pointed out that, in Menger spaces under Min and similar t-norms, the contractions of Sehgal and Bharucha-Reid are also ordinary contractions on related metric spaces. |
Clasificación UNESCO |
120804 |
Palabras clave español |
Espacios métricos ; Espacios probabilísticos ; Aplicación contractiva ; Estudio comparativo |
Código MathReviews |
MR1004655 |
Código Z-Math |
Zbl 0689.60019 |
Acceso al artículo completo |