Each quarter, the Editors of Fixed Point Theory and Applications will select an Editorial Board member or author to shine a spotlight on for their valuable contributions to the journal and the mathematics community as a whole. This quarter's Editorial Board member is William Art Kirk.
It is a fact that no one can contest that William Art Kirk is one of the founders of the modern theory of metric fixed points. With more than 175 works in the field of fixed point theory and 3500 citations, W.A. Kirk influenced the development of this flourishing field in a decisive way.
The very first and, maybe, most notable result in fixed point theory was given by his famous result on the existence of fixed points for nonexpansive mappings in reflexive Banach spaces with normal structure, published in Amer. Math. Monthly in 1965. This wonderful result opened a large gate to a whole new world to be explored, where geometry of the Banach spaces, nonexpansive mappings and fixed points were interconnected in a very unexpected and fruitful way. Later, in some papers with Kazimierz Goebel, weaker forms of nonexpansivity (such as asymptotically nonexpansive mappings) were also introduced and studied, aspects which are even today a source of inspiration for new generations of mathematicians.
Another significant moment in the fast development of the field is related to his fundamental book on metric fixed point theory, written jointly with Kaz Goebel „Topics in Metric Fixed Point Theory", and published in 1990.
Art Kirk continues to work and to publish new and relevant results in metric fixed point theory. As a consequence, the decision to highlights William Art Kirk contributions is a fortunate initiative of the journal Fixed Point Theory and Applications.