Orbital Continuity and Common Fixed Points in Menger PM-Spaces


Rale M. Nikolić, Vladimir T. Ristić, Jasmina Fijuljanin, Aleksanar Šebeković




In this paper, we prove that if a pair of semi R-commuting self-mappings defined on Menger PM-spaces with a nonlinear contractive condition posses a unique common fixed point, then these mappings are orbitally continuous. Also, we investigate whether this assertion and it converse holds if we replace semi R-commutativity with some other concept of commutativity in the weaker sense.