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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.42 no.2 Bogotá July/Dec. 2008

 

A result for approximating fixed points of generalized weak contraction of the integral-type by using Picard iteration

Un resultado para aproximar puntos fijos de contracción generalizada débil de la integral-tipo usando iteración de Picard

MEMUDU OLAPOSI OLATINWO1

1Obafemi Awolowo University, Ile-Ife, Nigeria. Email: polatinwo@oauife.edu.ng


Abstract

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.

Resumen

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.


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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 ]

[4] Berinde, V., `A priori and a posteriori error estimates for a class of φ-contractions´, Bulletins for Applied & Computing Math. 90, B (1999), 183-192.

[5] Berinde, V., Iterative Approximation of Fixed Points, Editura Efemeride, Baia Mare, 2002.         [ Links ]

[6] Berinde, V., `Approximating fixed points of weak contractions using Picard iteration´, Nonlinear Analysis Forum 9, 1 (2004), 43-53.         [ Links ]

[7] Branciari, A., `A fixed point theorem for mappings satisfying a general contractive condition of integral type´, Int. J. Math. Math. Sci. 29, 9 (2002), 531-536.         [ Links ]

[8] Chatterjea, S. K., `Fixed-point theorems´, C. R. Acad. Bulgare Sci. 10, (1972), 727-730.         [ Links ]

[9] Ciric, L. B., `Generalized contractions and fixed point theorems´, Publ. Inst. Math. (Beograd) (N. S.) 12, 26 (1971), 19-26.         [ Links ]

[10] Ciric, L. B., `A generalization of Banach's contraction principle´, Proc. Amer. Math. Soc. 45, (1974), 267-273.         [ Links ]

[11] Kannan, R., `Some results on fixed points´, Bull. Calcutta Math. Soc. 10, (1968), 71-76.         [ Links ]

[12] Rhoades, B. E., `A comparison of various definitions of contractive mappings´, Trans. Amer. Math. Soc. 226, (1977), 257-290.         [ Links ]

[13] Rhoades, B. E., `Two fixed point theorems for mappings satisfying a general contractive condition of integral type´, Int. J. Math. Math. Sci. 63, (2003), 4007-4013.         [ Links ]

[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 ]

(Recibido en julio de 2007. Aceptado en agosto de 2008)

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}
}

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