In this paper, we present a variant of Krasnoselskii's fixed point theorem in the case of ordered Banach spaces, where the order is generated by a normal and minihedral cone. In such a structure, there is a possibility to give a new sence to the concept of contraction.

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Abstract. In this paper, we study existence of positive solutions to the system of three-point fractional boundary value problem Mathematics subject classification (2010): 26A33, 34B16, 34B18, 34B27.

Abstract. We provide in this paper existence results for positive solution to the abstract Hammerstein equation NF u = u where N : E → E is a completely continuous operator, F : C → C is a continuous and bounded map and C is a cone in the Banach space E. The obtained results are used to prove existence results for positive solution to φ-Laplacian boundary value problem.Mathematics Subject Classification. 47H11, 34B15.