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Papers by Aneta Sikorska-nowak

Research paper thumbnail of Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces

International Journal of Mathematics and Mathematical Sciences, 2007

We prove two existence theorems for the integrodifferential equation of mixed type:x'(t)=f(t,... more We prove two existence theorems for the integrodifferential equation of mixed type:x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds),x(0)=x0, where in the first part of this paperf, g, h, xare functions with values in a Banach spaceEand integrals are taken in the sense of Henstock-Kurzweil (HK). In the second partf, g, h, xare weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functionsf, g, h, xsatisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.

Research paper thumbnail of Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces

International Journal of Mathematics and Mathematical Sciences, 2007

We prove two existence theorems for the integrodifferential equation of mixed type:x'(t)=f(t,... more We prove two existence theorems for the integrodifferential equation of mixed type:x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds),x(0)=x0, where in the first part of this paperf, g, h, xare functions with values in a Banach spaceEand integrals are taken in the sense of Henstock-Kurzweil (HK). In the second partf, g, h, xare weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functionsf, g, h, xsatisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.