Best proximity point results for almost contraction and application to nonlinear differential equation. (English) Zbl 1474.54167
Summary: V. Berinde [Nonlinear Anal. Forum 9, No. 1, 43–53 (2004; Zbl 1078.47042)] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost \(\Theta\)-contraction mappings and
to prove some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued \(\Theta\)-contraction mappings are obtained. Moreover, we give an example to support the results presented herein. An application to a nonlinear differential equation is also provided.
Citations:
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