Inequalities Applicable to Mixed Volterra-Fredholm Type Integral Equations
DOI:
https://doi.org/10.5644/SJM.06.2.10Keywords:
Inequalities, mixed Volterra-Fredholm type, integral equations, explicit estimates, discrete analogues, approximate solutionAbstract
In this paper we establish some new integral inequalities with explicit estimates which can be used as tools in the study of some basic properties of solutions of mixed Volterra-Fredholm type integral equations. Discrete analogues of the main results and some applications of one of our results are also given.
2000 Mathematics Subject Classification. 65R20, 45G10
Downloads
References
H. Brunner, On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods, SIAM J. Numer. Anal., 27 (1990), 987–1000.
H. Brunner and E. Messina, Time stepping methods for Volterra-Fredholm integral equations, Rend. Mat. Appl. Ser. VII, 23 (2003), 329–342.
C. Corduneanu, Integral Equations and Applications, Cambridge University Press, Cambridge, 1991.
O. Diekmann, Thresholds and travelling waves for the geographical spread of infection, J. Math. Biol., 6 (1978), 109–130.
V. P. Mikhailov, Partial Differential Equations, Mir Publishers, Moscow, 1978.
B. G. Pachpatte, Inequalities for Differential and Integral Equations, Academic Press, New York, 1998.
B. G. Pachpatte, Inequalities for Finite Difference Equations, Marcel Dekker, Inc., New York, 2002.
B. G. Pachpatte, Integral and Finite Difference Inequalities and Applications, NorthHolland Mathematics Studies, Vol. 205, Elsevier Science, B.V., Amsterdam, 2006.
B. G. Pachpatte, On mixed Volterra-Fredholm type integral equations, Indian J. Pure Appl. Math., 17 (1986), 488–496.
B. G. Pachpatte, On a parabolic type Fredholm integrodifferential equation, Numer. Funct. Anal. Optim., 30 (2009), 136–147.
H. R. Thieme, A model for the spatial spread of an epidemic, J. Math. Biol., 4 (1977), 337–351.
A. M. Wazwaz, A reliable treatment for mixed Volterra-Fredholm integral equations, Appl. Math. Comput., 127 (2002), 405–414.
