Some Fixed Point Theorems and Application to Biological Model

REFERENCES

• O. Arino , S. Gautier , and J.P. Penot ( 1984 ). A fixed point theorem for sequentially continuous mapping with application to ordinary differential equations . Functional Ekvac. 27 ( 3 ): 273 – 279 .
   Google Scholar
• A. Ben Amar , A. Jeribi , and M. Mnif ( 2005 ). On generalization of the Schauder and Krasnosel'skii fixed point theorems on Dunford–Pettis space and applications . Math. Meth. Appl. Sci. 28 : 1737 – 1756 .
   Web of Science ®Google Scholar
• C.S. Barroso and E.V. Teixeira ( 2004 ). A fixed point theorem for sum of operators and applications. (in press) .
   Google Scholar
• M. Boulanouar and L. Leboucher ( 1995 ). Une équation de transport dans la dynamique de population cellulaires . C. R. Acad. Sci. Paris 321 ( I ): 305 – 308 .
   Google Scholar
• M. Cessenat ( 1985 ). Théorèmes de trace pour des espaces de fonctions de la neutronique . C. R. Acad. Sci. Paris 300 ( I ): 89 – 92 .
   PubMed Web of Science ®Google Scholar
• M. Cessenat ( 1984 ). Théorèmes de trace L p pour des espaces de fonctions de la neutronique . C. R. Acad. Sci. Paris 299 ( I ): 831 – 834 .
   Google Scholar
• J.B. Conway ( 1990 ). A Course in Functional Analysis . Springer-Verlag , Berlin .
   Google Scholar
• R. Dautray and J.L. Lions ( 1988 ). Analyse Mathématiques et Calcul Numérique . Tome 9. Masson , Paris .
   Google Scholar
• J. Diestel ( 1980 ). A survey of results related to Dunford–Pettis property . In: Cont. Math. 2, Amer. Math. Soc. of Conf. on Integration, Topology and Geometry in Linear Spaces , pp. 15 – 60 .
   Google Scholar
• P. Dodds and J. Fremlin ( 1979 ). Compact operator in Banach lattices . Isr. J. Math. 34 : 287 – 320 .
   Web of Science ®Google Scholar
• N. Dunford and B.J. Pettis ( 1940 ). Linear operations on summable functions . Trans. Am. Math. Soc. 47 : 323 – 392 .
   Google Scholar
• N. Dunford and J.T. Schwartz ( 1958 ). Linear Operators: Part I General Theory . Pure and Applied Mathematics, Vol. 7. Interscience Publishers, New York .
   Google Scholar
• A. Grothendieck ( 1953 ). Sur les applications linéaires faiblement compactes d'espaces du type C(K) . Can. J. Math. 5 : 129 – 173 .
   Web of Science ®Google Scholar
• B. Lods ( 2004 ). On linear kinetic equations involving unbounded cross-sections . Math. Mode. Meth. Appl. Sci. 27 : 1049 – 1075 .
   Web of Science ®Google Scholar
• K. Latrach ( 1996 ). On a nonlinear stationary problem arising in transport theory . J. Math. Phys. 37 : 1336 – 1348 .
   Web of Science ®Google Scholar
• K. Latrach and A. Jeribi ( 1999 ). A nonlinear boundary value problem arising in growing cell populations . Nonlinear Anal. T.M.A. 36 : 843 – 862 .
   Web of Science ®Google Scholar
• J.L. Lebowitz and S.I. Rubinow ( 1974 ). A theory for the age and generation time distribution of microbial population . J. Math. Biol. 1 : 17 – 36 .
   Web of Science ®Google Scholar
• M. Rotenberg ( 1983 ). Transport theory for growing cell populations . J. Theo. Biol. 103 : 181 – 199 .
   PubMed Web of Science ®Google Scholar
• C. Van der Mee and P. Zweifel ( 1987 ). A Fokker–Plank equation for growing cell population . J. Math. Biol. 25 : 61 – 72 .
   PubMed Web of Science ®Google Scholar
• R.E. Showalter ( 1997 ). Monotone operators in Banach space and nonlinear partial differential equations . AMS .
   Google Scholar
• E. Zeidler ( 1986 ). Nonlinear Functional Analysis and Its Applications. Vol. I . Springer , New York .
   Google Scholar