Technically, PALMS CENTER was Houston's first shopping mall. It opened in September 1955, one year before business began at GULFGATE CENTER. PALMS CENTER encompassed 268,000 square feet and forty-one tenant spaces. Size-wise, the entire shopping plaza could have nearly fit into one of the GULFGATE anchor stores.   
Photo from https://arch-ive.org / "Houston Arch-ive"

An aerial view of GULFGATE SHOPPING CITY. The sprawling open-air facility was anchored by San Antonio-based Joske's and Houston-based Sakowitz. It also housed a Weingarten's supermarket.
Photo from Colourpicture Publishers, Incorporated

The ginormous Joske's at GULFGATE featured three shopping levels and 208,000 square feet of selling space.

Photo from Allied Stores Corporation Annual Report 1956 

In this vintage South Wing view, a J.J. Newberry 5 & dime is on the left, with a W.T. Grant ("Grants") variety store on the right.
Photo from Colourpicture Publishers, Incorporated