Best proximity for proximal operators on $b$-metric spaces

Authors: ARIANA PITEA, MONICA STANCIU

Abstract: 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.

Keywords: Best proximity point, generalized proximal contraction, $b$-metric space

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