A new multiple fixed point theorem with applications

Yıl 2021, Cilt: 5 Sayı: 3, 393 - 411, 30.09.2021

Svetlin Georgiev , Karima Mebarki

https://doi.org/10.31197/atnaa.791033

Öz

The purpose of this work is to establish an extension of a Bai-Ge type multiple fixed point theorem for a sum of two operators. The arguments are based upon recent
fixed point index theory in cones of Banach spaces for a k-set contraction perturbed by an expansive operator. As illustration, our approach is applied to prove the
existence of at least three nontrivial non-negative solutions for a class eigenvalue three-point BVPs for a class of fourth order ordinary differential equations (ODEs
for short).

Anahtar Kelimeler

fixed point index, sum of operators, cone, positive solution

Kaynakça

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