Yes they do. ASICS tennis shoes use something called GEL cushioning. Depending on what kind of shoe you buy, you can get cushioning in the heel, forefoot or both.
If your doctor recommended the Asics Kayano running shoe, the best is the Asics Gel Kayano 17. It is available for men and women in many colors. The shoe has been rated as the highest quality with most stability and cushioning.
The Asics Piranha SP3 running shoes have received good reviews in general. They have a lightweight sole which is aimed to provide maximum cushioning and comfort together with a breathable upper layer.
The Asics Cumulus 10 are one of the best running shoes. They offer amazing cushioning and have greater impact absorption. You can get them at a great price of $85 online.
By experience running in these shoes I wouldn't recommend jumping in these, you can feel your feet while you jump. The cushioning is great for running, but not as much as jumping.
In my opinion, a good pair of shoes that you could get for running is the Asics Gel Evolution 5 or the Asics GT-2160. If you do not feel like these shoes are the good for you, simply visit (http://www.runningshoesexpert.com/) to get a little list of some of the best rated shoes. There is also an online tool to help you to determine what shoes are the best for you, on the website.
The asics kinetic shoes do provide the comfort and support for both heel and toe. The shoe is designed with cushion in the forefoot to support the foot from any irritation and better comfort.
Based on their product description, I would say they are good running shoes. They are light, have sufficient cushioning for your feet for superior impact protection. It's a very stable and protective shoe.
Asics 2160 are good and recommended women's shoes. They are great for running and exercising. They are good for your feet and you can buy them online or at a footlocker.
I got Asics gel Kayano running shoes for my brother and he loved it. He said they were comfortable and soft, so judging from his reaction, I believe the Asics gel Kayano running shoes are a good brand.
www.onlineshoes.com/Asics has good reviews on their shoes. www.calibex.com/Shoes has some. www.designerapparel.com/Asics is having a sale. There are also plenty on Amazon and Ebay!
There are several ASICS shoes that have gel in the underfoot of shoes. In fact, ASICS has entire lines of shoes called ASICS Gel-Equation, Gel-Foundation, Gel-Kayano, Gel-Nimbus and Gel-Candice. The Men's ASICS Gel-Kayano shoe has a guidance trusstic and line systems and is made out of synthetics and mesh. The Women's Gel-Nimbus running shoe has a "rearfoot and forefoot" GEL cushioning system that absorbs shock while running. It is made out synthetics and fabrics.
I go to the rate my shoes site to read reviews on shoes including the asics control shoes. That shoe is nice and had good reviews. Other shoes can be found also.