## Luong V. Nguyen, Nguyen T.N. Tram, Fixed point results with applications to involution mappings

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DOI: 10.23952/jnva.4.2020.3.06
Volume 4, Issue 3, 1 December 2020, Pages 415-426

Abstract. In this paper, we first introduce a class of functions with the property $(L)$, which is weaker than lower semicontinuity property. We then prove a general result on the existence of fixed points of a mapping $T$ in a complete metric $(X,d)$ under the assumption that the function $x\to d(x,Tx)$ has the property. This result generalizes several results in the literature. Finally, we apply our result to the existence of fixed points of involution mappings. Examples are given to illustrate our results.