The paper presents existence results of $(\phi,\varphi)$ best proximity points for operators that fulfill implicit type inequalities. Classes of mappings endowed with continuity, monotone or monotone-type properties, and which additionally satisfy some adequate inequalities are studied from this point of view. Applications of our results are given with regard to fixed point theory.
Best proximity point, generalized proximal contraction, $b$-metric space
PITEA, ARIANA and STANCIU, MONICA
"Best proximity for proximal operators on $b$-metric spaces,"
Turkish Journal of Mathematics: Vol. 47:
7, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss7/3