Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations

Nonlinear Analysis

Moosa Moosa Gabeleh¹  Seithuti Philemon Moshokoa²  Calogero Vetro³ 

[1] Ayatollah Boroujerdi University;Tshwane University of Technology;University of Palermo;

关键词: best proximity pair;    noncyclic φ-condensing operator;    ordinary differential equations;    strictly convex Banach space;   

DOI  :  10.15388/NA.2019.24.6.14907

来源: DOAJ

【 摘 要 】

We establish a best proximity pair theorem for noncyclic φ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic φ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations.

【 授权许可】

Unknown