AN INTEGRAL EQUATION RELATED TO AN EPIDEMIC MODEL VIA WEAKLY PICARD OPERATORS TECHNIQUE IN A GAUGE SPACE

作者：Olaru Ion Marian^*

来源：Fixed Point Theory, 2014, 15(1): 179-188.

• Picard operator
• gauge spaces
• fixed point
• integral equation

In the paper Qualitative behavior of an integral equation related to some epidemic model (Demonstratio Mathematica, Vol. XXXVI, No 3/2003, 603-609) the author Eva Brestovanska has considered the integral equation
x(t) = [g1 (t) + f(0)(t) A(1)(t - s)F-1(s, x(s))ds]center dot center dot center dot[g(p) (t) + f(0)(t) A(p) (t - s)F-p(s, x(s))ds], t >= 0.
In this paper we shall study by weakly Picard technique operators in a gauge space: the existence, uniqueness and data dependence such as the continuity, smooth dependence on parameter for the solution of the following integral equation
x(t) = [g1 (t) + f(0)(t) K-1(t, s, x(s))ds]center dot[g2 (t) + f(0)t K-2(t, S, X(S))], t is an element of [0, infinity).
Our approach are connected with some results due from I.M. Olaru (An integral equation via weakly Picard operators, Fixed Point Theory, Vol 11 No1/2010, 97-106 and Generalization of an integral equation related to some epidemic models, Carpathian J. Math. Vol 26, No.1(2010), 92-96).

• 出版日期2014