L^P solutions to the parameterized Fredholm integral equations associated with Chandrasekhar kernels

References

• Garabedian PR. Partial differential equations. New York: Wiley; 1964.
   Google Scholar
• Atkinson KE. The solution of nonunique linear integral equations. Numer Math. 1967;10:117–124.
   Web of Science ®Google Scholar
• Douglas JR J. Mathematical programming and integral equations. Symposium on the Numerical Treatment of Ordinary Differential Equations, Integral and Integro-Differential Equations; Basel: Birkhauser; 1960. p. 269–274.
   Google Scholar
• Kammerer WJ, Nashed MZ. Iterative methods for best approximate solutions of linear integral equations of the first and second kinds. J Math Anal Appl. 1972;40:547–573.
   Web of Science ®Google Scholar
• Cimmino G. Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari, La Ricerca Scientifica 1938-XVI, Serie II, Anno IX, Vol. 1, Roma: p. 326–333.
   Google Scholar
• Lonseth AT. Approximate solutions of Fredholm-type integral equations. Bull Amer Math Sot. 1954;60:415–430.
   Web of Science ®Google Scholar
• Mikhlin SG, Smolitskip KL. Approximate methods for solution of differential and integral equations. New York: American Elsevier; 1967.
   Google Scholar
• Petryshyn WV. On a general iterative method for the approximate solution of linear operator equations. Math Camp. 1963;17:1–10.
   Google Scholar
• Rxll LB. Error bounds for iterative solutions of Fredholm integral equations. Pac J Math. 1955;5:977–986.
   Google Scholar
• Walther A, Dejon B. General report on the numerical treatment of integral and integro-differential equations. Symposium on the Numerical Treatment of Ordinary Differential Equations, Integral and Integro-Differential Equations; Basel: Birkhauser; 1960. p. 645–671.
   Google Scholar
• Kulkarni RP. A superconvergence result for solutions of compact operator equations. Bull Austral Math Soc. 2003;68:517–528.
   Web of Science ®Google Scholar
• Kulkarni RP. Approximate solution of multivariable integral equations of the second kind. J Inte Equ Appl. 2004;16:343–374.
   Google Scholar
• Atkinson KE. The numerical solution of integral equations of the second kind. New York: Cambridge University Press; 1997.
   Google Scholar
• Atkinson KE, Chandler G. The collocation method for solving the radiosity equation for unoccluded surfaces. J Integral Equ Appl. 1998;10:253–290.
   Google Scholar
• Brakhage H. Uber die numerische behandlung von integralgleichungen nach der quadraturformelmethode. Numer Math. 1960;2:183–196.
   Google Scholar
• Atkinson KE. Iterative variants of the Nyström method for the numerical solution of integral equations. Numer Math. 1973;22:17–31.
   Web of Science ®Google Scholar
• Kelley C. A fast multilevel algorithm for integral equations. SIAM J Numer Anal. 1995;32:501–513.
   Web of Science ®Google Scholar
• Hackbusch W. Multi-grid methods and applications. Berlin: Springer-Verlag; 1985.
   Google Scholar
• Hackbusch W. Integral equations, theory and numerical treatment. Basel: Birkhauser-Verlag; 1994.
   Google Scholar
• Chang DC, Feng SY. On the integral equations of Chandrasekhar type. J Nonl Conv Anal. 2018;19:525–541.
   Web of Science ®Google Scholar
• Chen Q, Yang B. A survey on the study of Hilbert-type inequalities. J Ineq Appl. 2015;2015:1.
   Google Scholar
• Yang B. On the norm of operator and Hilbert-Type inequalities. Beijing: Science Press; 2009.
   Google Scholar
• Weyl H. Singulare integral Gleichungen mit besonderer Berücksichtigung des Fourierschen integral theorems. Gottingen: Inaugeral-Dissertation; 1908.
   Google Scholar
• Schur I. Bemerkungen für Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen. J Math. 1911;140:1–28.
   Google Scholar
• Hardy GH. Note on a theorem of Hilbert concerning series of positive term. Proc Lond Math Soc. 1925;23:45–46.
   Google Scholar
• Hardy GH, Littlewood JE, Pólya G. Inequalities. Cambridge: Cambridge University Press; 1934.
   Google Scholar
• Yang B. On the norm of an integral operator and applications. J Math Anal Appl. 2006;321:182–192.
   Web of Science ®Google Scholar
• Feng SY, Chang DC. An existence and uniqueness result for parameterized integral equations with Chandrasekhar kernels. J Nonl Conv Anal. 2018;19:2053–2068.
   Web of Science ®Google Scholar
• Feng SY, Chang DC. Exact bounds and approximating solutions to the Fredholm integral equations of Chandrasekhar type. Taiwan J Math. 2019;23:409–425.
   Web of Science ®Google Scholar
• Feng SY, Chang DC. Existence, uniqueness, and approximation solutions to linearized Chandrasekhar equation with sharp bounds. Anal Math Phys. 2020;10:17. Available from: https://doi.org/10.1007/s13324-020-00359-2.
   Web of Science ®Google Scholar
• Zorich VA. Mathematical analysis (Part II). 4th corrected edition, Moscow (2002): Springer; 2004.
   Google Scholar