title: Existence of common fixed point and best proximity point for generalized nonexpansive type maps in convex metric space.
abstract: 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.
authors.affiliation: Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana 124001 India.
authors.forename: Savita
authors.initials: S
authors.lastname: Rathee
authors.affiliation: Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana 124001 India.
authors.forename: Kusum
authors.initials: K
authors.lastname: Dhingra
authors.affiliation: Department of Mathematics, Government College Bahu, Jhajjar, Haryana 124142 India.
authors.forename: Anil
authors.initials: A
authors.lastname: Kumar
keywords: Best proximity point; Common fixed point; Common property (E.A.); Compatible maps; pq-affine; q-affine