Revista de la
Unión Matemática Argentina
On some fixed point theorems in abstract duality pairs
Kinga Cichoń, Mieczysław Cichoń, and Mohamed M. A. Metwali
Volume 61, no. 2 (2020), pp. 249–266

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We study the existence of fixed points for some functional problems. We focus on bilinear operators which are extensions of the product of operators (Banaś–Dhage-type results) and obtain some results on abstract duality pairs (abstract triples). However, we do not restrict ourselves to these cases; in fact, some special cases which do no fit in the above description are indicated. In particular, our approach allows us to study some differential or integral problems, for which the operators are not acting on a fixed Banach space.