Leray–Schauder and Furi–Pera types fixed point theorems for the sum of two weakly sequentially continuous mappings and application to transport equation

摘要

In the present paper, we establish some new variants of Leray–Schauder type fixed point theorems for the sum of two weakly sequentially continuous mappings, A and B defined on a closed convex subset Ω of a Banach space E, where A satisfies some conditions and B is a separate contraction (resp. nonlinear contraction) mapping. Note here that Ω need not to be bounded. Moreover, we give Leray–Schauder and Furi–Pera fixed point theorems for a larger class of weakly sequentially continuous mappings under weaker assumptions and we explore this kind of generalization by looking for the multivalued mapping (I ? B)~(?1)A, when I ?B may not be injective. An illustrative application to a source problem in L1 setting with general boundary conditions is presented.