In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of Dhage in a partially ordered normed linear space. The approximation of the solutions are obtained under weaker mixed partial continuity and partial Lipschitz conditions. Our hypotheses and abstract results are also illustrated by some numerical examples.
Dhage,B . (2017). Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations. International Journal of Nonlinear Analysis and Applications, 8(1), 95-112. doi: 10.22075/ijnaa.2017.997.1194
MLA
Dhage,B . "Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations", International Journal of Nonlinear Analysis and Applications, 8, 1, 2017, 95-112. doi: 10.22075/ijnaa.2017.997.1194
HARVARD
Dhage B. (2017). 'Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations', International Journal of Nonlinear Analysis and Applications, 8(1), pp. 95-112. doi: 10.22075/ijnaa.2017.997.1194
CHICAGO
B Dhage, "Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations," International Journal of Nonlinear Analysis and Applications, 8 1 (2017): 95-112, doi: 10.22075/ijnaa.2017.997.1194
VANCOUVER
Dhage B. Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations. IJNAA. 2017;8(1):95-112. doi: 10.22075/ijnaa.2017.997.1194
International Journal of Nonlinear Analysis and Applications