On locally condensing operators (Q413595)

The author introduces the concept of a locally strongly condensing operator, which is a modification of the definition of locally strictly condensing operators given by \textit{R. D. Nussbaum} [``The fixed point index for local condensing maps'', Ann. Mat. Pura Appl., IV. Ser. 89, 217--258 (1971; Zbl 0226.47031)]. The author shows that such operators form a linear space, a semigroup and a right near-ring. Some applications of such operators to nonlinear equations are given.