- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 5 Issue: 3
- A new multiple fixed point theorem with applications
A new multiple fixed point theorem with applications
Authors : Svetlin GEORGİEV, Karima MEBARKİ
Pages : 393-411
Doi:10.31197/atnaa.791033
View : 3 | Download : 7
Publication Date : 2021-09-30
Article Type : Research
Abstract :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).Keywords : fixed point index, sum of operators, cone, positive solution