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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.42 no.2 Bogotá July/Dec. 2008
1Obafemi Awolowo University, Ile-Ife, Nigeria. Email: polatinwo@oauife.edu.ng
Following concepts of A. A. Branciari and B. E. Rhoades, of in this paper, we shall establish a fixed point theorem by using a generalized weak contraction of integral type. Our result is a generalization of the classical Banach's fixed point theorem and other related results.
Key words: Fixed points, weak contraction of integral type, Picard iteration.
2000 Mathematics Subject Classification: 47H06, 47H10.
Siguiendo conceptos de A. A. Branciari, y B. E. Rhoades, en este artículo establecemos un teorema de punto fijo usando una contracción débil generalizada de tipo integral. Nuestro resultado es una generalización del clásico teorema del punto fijo de Banach y de otros resultados relacionados.
Palabras clave: Puntos fijos, contracción débil de tipo integral, iteración de Picard.
Texto completo disponible en PDF
References
[1] Agarwal, R. P., Mechan, M. & O'Regan, D., Fixed Point Theory and Applications, Cambridge University Press, 2001. [ Links ]
[2] Banach, S., `Sur les operations dans les ensembles abstraits et leur applications aux equations integrales´, Fund. Math. 3, (1922), 133-181. [ Links ]
[3] Berinde, M. & Berinde, V., `On a general class of multi-valued weakly Picard mappings´, J. Math. Anal. Appl. 326, (2007), 772-782. [ Links ]
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[5] Berinde, V., Iterative Approximation of Fixed Points, Editura Efemeride, Baia Mare, 2002. [ Links ]
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[12] Rhoades, B. E., `A comparison of various definitions of contractive mappings´, Trans. Amer. Math. Soc. 226, (1977), 257-290. [ Links ]
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[14] Zamfirescu, T., `Fix point theorems in metric spaces´, Arch. Math. 23, (1972), 292-298. [ Links ]
[15] Zeidler, E., Nonlinear Functional Analysis and its Applications-Fixed Point Theorems, Springer-Verlag, New York, 1986. [ Links ]
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv42n2a03,
AUTHOR = {Olatinwo, Memudu Olaposi},
TITLE = {{A result for approximating fixed points of generalized weak contraction of the integral-type by using Picard iteration}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2008},
volume = {42},
number = {2},
pages = {145-151}
}