Una aplicación de las funciones débilmente contractivas a problemas de valor en la frontera de funciones con valores en intervalos

• Angulo Castillo, Vladimir ^[1]
  1. [1] Universidad Industrial de Santander

     Universidad Industrial de Santander

     Colombia

     
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 32, Nº. 1, 2014 (Ejemplar dedicado a: Revista Integración), págs. 27-37
• Idioma: español
• Títulos paralelos:
  • An application of weakly contractive mappings to boundary value problems of interval-valued functions
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Se estudia la existencia y unicidad de soluciones para problemas de valor en la frontera asociadas a ecuaciones diferenciales de funciones con valores en intervalos, usando la derivada de Hukuhara y algunos teoremas de punto fijo de funciones débilmente contractivas definidas en conjuntos parcialmente ordenados.

  • English

    We study the existence and uniqueness of solutions for boundary value problems associated to differential equations of interval-valued functions, by using the derivative of Hukuhara and some fixed point theorems for weakly contractive mappings defined on partially ordered sets.

• Referencias bibliográficas
  • Citas [1] Aubin J.P. and Cellina A., Differential Inclusions, Springer-Verlag, New York, 1984.
  • [2] Aubin J.P. and Franskowska H., Set-Valued Analysis, Birkhäuser, Boston, 1990.
  • [3] Aubin J.P. and Franskowska H., “Set-valued analysis in control theory”, Set-Valued Anal. 8 (2000), 1–9.
  • [4] Banks H.T. and Jacobs M.Q., “A differential calculus for multifunctions”, J. Math. Anal. Appl., 29 (1970), 246–272.
  • [5] Folland G., Real Analysis. Pure and Applied Mathematics, John Wiley & Sons Inc., New York, 1999.
  • [6] Dhutta P.N. and Choudhury B.S., “A generalization of contraction principle in metric spaces”, Fixed Point Theory Appl. (2008), 8 p.
  • [7] Goetschel R. and Voxman W., “Elementary fuzzy calculus”, Fuzzy Sets and Systems 18 (1986), 31–43.
  • [8] Harjani J. and Sadarangani K., “Generalized contractions in partially ordered metric spaces and applications to ordinary differential...
  • [Revista Integración
  • Una aplicación de las funciones débilmente contractivas 37
  • [9] Hukuhara M., “Intégration des applications measurables dont la valeur est un compact convexe”, Funkcial. Ekvac. 10 (1967), 205–223.
  • [10] Kaleva O., “Fuzzy differential equations”, Fuzzy Sets and Systems 24 (1987), 301–317.
  • [11] Kaleva O., “A note on fuzzy differential equations”, Nonlinear Anal. 64 (2006), 895–900.
  • [12] Moore R.E., Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1966.
  • [13] Moore R.E., Computational Functional Analysis, Ellis Horwood Limited, England, 1985.
  • [14] Negoita C.V. and Ralescu D., Applications of Fuzzy Sets to Systems Analysis, Wiley, New York, 1975.
  • [15] Nieto J.J. and Rodríguez-López R., “Applications of contractive-like mapping principles to fuzzy equations”, Rev. Mat. Complut. 19 (2006),...
  • [16] Nieto J.J. and Rodríguez-López R., “Contractive mapping theorems in partially ordered sets and applications to ordinary differential...
  • [17] Nieto J.J. and Rodríguez-López R., “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential...
  • [18] Puri M. and Ralescu D., “Fuzzy random variables”, J. Math. Anal. Appl. 114 (1986), 409– 422.
  • [19] Puri M. and Ralescu D., “Differential of fuzzy functions”, J. Math. Anal. Appl. 91 (1983), 552–558.
  • [20] Rhoades B.E., “Some theorems on weakly contractive maps”, Nonlinear Anal. 47 (2001), 2683–2693.
  • [21] Zadeh L.A., “Fuzzy sets”, Infor. and Control 8 (1965), 338–353.