First I’m assuming that your artwork is a luxury item.  If so, then the answer is NO.  If you’re not sure if it’s a luxury item then you have bigger concerns and need to clarify your market.
Discounting luxury items is a very big mistake.  You’re asking people to pay a big premium for something that they don’t need and then changing your mind.  It’s very confusing.  No wonder people are reluctant to buy art.

Another important rule in business negotiation is that you should never give away something without receiving something in return.

Another option to discounting your art is to offer a friendly service. Offer to come hang your art on their wall, or provide them with complimentary, notice I didn’t say free, shipping, maybe donate 10% to their favorite charity.  This is called cause marketing.
Artists desperate to close a sale will often discount their prices.  Rather than doing this you should provide a range of price points for your collector to reach.  I start with a note card for $5 and go to $36,000 for my largest commissioned canvas and I maintain a price point everywhere in between.  This way I can make the conversation about the collector’s selection and not the price they’re going to pay.
Open up a Tiffany’s catalog.  They get this.  Tiffany’s offers beautiful Canary diamond engagement rings or a silver key chain with their logo, which is what the key chain buyer really wants. Tiffany’s knows their market.
It’s also important to remember if you work with a gallery they are selling your work at a retail price that you’ve established.  If you discount your work then you’re undercutting your representative. And that’s not cool.
Some galleries ask if they can negotiate a discount on your behalf.  This is your call but my answer is still no.  I think that it’s worth noting that an art consultant that I worked with in Los Angeles told me that the artists that she represented who did not discount always sold more work then those who did.

I have a deep appreciation for my collectors and out of respect for them I can’t offer one price to one and not to the others.  I don’t think it’s fair.  Maintain integrity in your business transactions and reflect that in your pricing.