in the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{kim} and textit{lee} [w.k. kim and k.h. lee, generalized fuzzy games and fuzzy equilibria, fuzzy sets and systems, 122 (2001), 293-301] and textit{tarafdar} [e. tarafdar, fixed point theorems i...

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

By the use of a generalized version of the Poincaré–Birkhoff fixed point theorem, we prove the existence of at least two periodic solutions for a class of Hamiltonian systems in the plane, having in mind the forced pendulum equation as a particular case. Our approach is closely related to the one used by Franks in [15], but the proof remains at a more elementary level. 2010 Mathematics Subject ...