A general concept of multiple fixed point for mappings defined on spaces with a distance

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion from [A. Roldan, J. Martinez-Moreno, C. Roldan,  Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl., 396 (2012), 536–545]. The obtained multiple fixed point theorems extend, generalise and unify many related results in literature.