Rebecca Davenport may paint brick walls and closed doors, but few doors are being slammed shut in her face these days.

While some local artists complain bitterly about the bleak prospects for success in the competitive art world, Davenport, a slender, straight-forward woman in her mid-30s, is gaining a national and international reputation. Working out of a studio in her apartment at the Beverly Court, an Adams-Morgan building long known as a residence of Washington artists, the Uppreville, Va., native has such "tremendous demand" for her paintings that she finds it "difficult to fill."

Davenport's "Walls" series, to be shown at Georgetown's Fendrick Gallery beginning Jan. 30, is the latest in a body of work that has included her own version of female pin-ups; "White Soul," paintings of rural Southerners; and "Davenports," portraits of the artist's friends seated on their living room sofas. When some of that last series was shown in 1977 in "Four Young Realists" at New York's ACA Gallery, New York Times art critic Hilton Kramer proclaimed that Davenport "dominated the show." Shortly afterward a self-portrait was chosen for "Selected 20th-Century Nudes," a New York exhibit that also included such well-known artists as Hans Hoffman, Willem de Kooning and Philip Pearlstein.

That year Davenport also became one of only two Americans to win prizes at the Festival Internationale de la Peinture, held each summer at Cagnes-sur-Mer, France. Her portrait of Washington gallery owner Rebecca Cooper placed third in the prestigious competition (former Washington resident Ed McGowin won fourth prize).

Last summer her work was shown again at Cagnes-sur-Mer and at Paris's Musee d'Art Moderne in an exhibition devoted to festival prize-winners from the previous five years. Those paintings are now being shown at the Federal Reserve System building on Constitution Avenue.

Following the abstract expressionism, color field painting and pop art of the '50s and '60s, Davenport's work is part of a renewed interest in realism that has grown in the quiet of the '70s. She distinguishes her paintings from those of the New Realists, or photorealists, by calling them "figurative or representational," explaining, "My paintings are based on photographs, but they're not reproductions of photographs. They're more subjective, more an expression of personal experience."

Although she is glad "no one 'ism' dominates art now and artists are freer to do what they want," she thinks people respond to her work in part because she "paints a recognizable image-some people find abstract art too impersonal and want something recognizable to relate to."

Her aim is not to give the public what it wants to see, but to "try to get them to look at things in a different, unique way, to see that what seems ugly, like a wall, may be beautiful, and vice versa. There's a nakedness about my paintings, whether they're of people or of objects."

It's objects, not people, that Davenport has been most interested in recently. She has just begun a new series-paintings of people's environments, of the rooms they live in.

"They're essentially portraits, too," she insists, "but portraits made up of objects people surround themselves with." The next step, Davenport hopes, will be an individual show of the "portraits" at a major New York gallery, and although nothing is definite, there have been several expressions of interest. It's just a matter of mine until all the doors are open. CAPTION: Picture, no caption