Existence of common fixed point and best proximity point for generalized nonexpansive type maps in convex metric space

Springerplus. 2016 Nov 9;5(1):1940. doi: 10.1186/s40064-016-3399-3. eCollection 2016.


Here, we extend the notion of (E.A.) property in a convex metric space defined by Kumar and Rathee (Fixed Point Theory Appl 1-14, 2014) by introducing a new class of self-maps which satisfies the common property (E.A.) in the context of convex metric space and ensure the existence of common fixed point for this newly introduced class of self-maps. Also, we guarantee the existence of common best proximity points for this class of maps satisfying generalized non-expansive type condition. We furnish an example in support of the proved results.

Keywords: Best proximity point; Common fixed point; Common property (E.A.); Compatible maps; pq-affine; q-affine.