Best proximity point for the sum of two non-self-operators (Q780513)

Summary: In the present paper, we focus our attention on the existence of the fixed point for the sum of the cyclic contraction and the noncyclic accretive operator. Also, we study the best proximity point for the sum of two non-self-mappings. Moreover, we provide the existence of the best proximity point for the cyclic contraction through the notion of the nonlinear \(\mathcal{D}\)-set contraction. Finally, we give the existence of the best proximity point for the sum of the nonlinear \(\mathcal{D}\)-set contraction mapping and partially completely continuous mapping in the setting of the partially ordered complete normed linear space.