Abstract
This chapter discusses Krasnoselskii-type fixed point results for monotone
operators. It is well known that the monotone operators are not continuous on the whole
domain, so we will find the solutions of discontinuous operator equations and inclusions.
The presented fixed point results may be considered as variants of the Krasnoselskii fixed
point theorem in a more general setting. The results of Darbo, Schauder and
Bohnentblust-Karlin are also generalized. We prove these results for the case of single-valued and set-valued monotone operators. We use our main result for single-valued
operators to obtain the existence of solutions of anti-periodic ABC fractional BVP. The
fixed point result for set-valued monotone operators is used to discuss the existence of
solutions of a given fractional integral inclusion in ordered Banach spaces.
Keywords: Krasnoselskii's fixed point theorem, Set valued mappings, Convex, Compact, Closed sets, Banach spaces, Fractional differential equations, Atangana and Baleanu derivatives.
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