The method of Kantorovich majorants to nonlinear singular integral equations with Hilbert kernel

• M. H Saleh ^[1] ; S. M Amer ^[1] ; M. H Ahmed ^[1]
  1. [1] Zagazig University

     Zagazig University

     Egipto

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 12, Nº. 2, 2010, págs. 29-42
• Idioma: inglés
• DOI: 10.4067/S0719-06462010000200003
• Enlaces
  • Texto completo
• Resumen
  • español

    Este artículo es concerniente a la aplicabilidad del método de mayorantes de Kantorovich para ecuaciones integrales singulares no lineales con núcleo de Hilbert. Los resultados son aplicaciones en espacios de Hölder.

  • English

    This paper concerned with applicability of the method of Kantorovich majorants to nonlinear singular integral equations with Hilbert kernel . The results are illustrated in Hölder space.

• Referencias bibliográficas
  • Ahmed, N. U. (1991). Semigroup Theory with Applications to Systems and Control. Longman Scientific & Technical, Harlow; John Wiley &...
  • Ahmed, N. U.. (2006). Dynamic Systems and Control with Applications. World Scientific Publishing Co. Pte. Ltd.. HackensackNJ.
  • Ahmed, N. U. (2001). Systems governed by impulsive differential inclusions on Hilbert spaces. Nonlinear Anal. 45. 693-706
  • Amer, S.M,Dardery, S. (2005). On the theory of the of nonlinear singular integral equations with shift in Hölder spaces. Forum Math. 17. 753-780
  • Amer, S.M,Nagdy, A.S. (2000). On the modified Newton’s approximation method for the solution of nonlinear singular integral equations. Hokkaido...
  • Amer, S.M.. (1996). On the approximate solution of nonlinear singular integral equations with positive index. Int. J. Math. Math. Sci. 19....
  • Appel, J. W,Pascale, E. De,Eevkhuta, N. A,Zabrejko, P. P. (1995). On the two-step Newton method for the solution of nonlinear operator equations....
  • Argyro, Ioannis K. (2007). Othe convergence of Newton’s method for a class of nonsmooth operators. Journal of Computational and Applied Mathematics....
  • Espedito de Pascale-Pjptr, P. (1998). Zabrejko, New convergence criteria for the Newton-Kantorovich method nd some applications to nonlinear...
  • Cianciaruo, Filomena,De Pascale, Espedito. (2006). Estimates of majorizing sequences in the Newton-Kantorovich method: Afurther improvement....
  • Gakhov, F.D. (1990). Boundary Value Problems. Dover Publ. N.Y.
  • Guseinov, A.I,Mukhtarov, kh. (1980). sh., Introduction to the Theory of Non-linear Singular Integral Equations, (In Russian. Nauk.
  • Jinyuan, D. (2000). The collocation methods and singular integral equations with Cauchy kernel. Acta Math.Sci.. 20. 289-302
  • Kantorovich, L.V,Akilov, G.P. (1982). Functional Analysis. Pergamon Press. Oxford.
  • Ladopoulos, E.G,Zisis, V.A. (1996). Non-linear singular integral approximations in Banach spaces. Non-linear Analysis,Theory,Methods and Applications....
  • Mikhlin, S.G,Prossdorf, S. (1986). Singular Integral Operator. Akademie- Verlag,Berlin.
  • Muskhelishvill, N.I. (1968). Singular Integral Equations: Englih Trans I. Noordhoff Ltd.Groningen.
  • Pedas, A,Vainikko, G. (1997). Supper convergence of piecwise polyn-omial colloctions for nonlinear weakly singular integral equtions. Journal...
  • Pogorzelski, W. (1966). Integral Equations and Their Applications. Oxford Pergamon Press and Warszawa, PWN.
  • Qingbiao, Wu,Yueqing, Zhao. Newton-Kantorovich convergence theorem for the inversefree Jarratt method in Banach space. Applied Mathematics...
  • Qingbiao, Wu,Yueqing, Zhao. (2006). Third-order convergence theorem by using majorizing function for a modified Newton method in Banch space....
  • Saleh, M.H,Amer, S.M. (2008). On the mechanical qudrature method for solving singular integral equations with Hilbert kernel. Journal of concrete...
  • Subhra, Bhattachrya,Maudel, B.N. (2008). Numerical solution of a singular integro-differential equations. Applied Mathematics and Computation....