The Gunners have enjoyed a solid start to the season at the back, conceding just one goal in their opening four Premier League matches.
Arteta believes both players have been playing at an extremely high level, particularly Jenkinson, who has stepped up in the absence of Bacary Sagna, and hopes they can continue that for the foreseeable future.
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He told the club's official website: "I think they’ve been very consistent. I think Gibbsy has been playing really well. I think he’s finding himself more comfortable going forwards.
"He’s rapid and can make a big difference. It’s tough for a wide man to defend [against] a full-back like him.
"Carl is finding himself more comfortable. He’s had four or five games under his belt, he’s done a whole pre-season with us and you can see he’s confident.
"Against Montpellier he put a brilliant cross in for Gervinho to score the goal.
"That’s what we need because we’re missing players. When you’re replacing someone like Bac [Sagna] it’s not easy because you’re under a lot of pressure. I think they’ve been really good.
"The challenge is to maintain the level and to keep up to the high level. I think that’s very difficult, but Carl’s done that in the last few games and hopefully he can maintain that."