Famous from a Cartier-Bresson picture these are the Camondo stairs. They are opposite a street between Bankalar Caddesi 9 ands 11. I found on the web:

"According to a plaque on the stairs: “Camondo Stairs had been constructed by the Camondo Family around 1870-1880 and repaired by the Beyoglu Municipality Quincentennial Foundation.”

About the family that build the stairs (From ricciarmani.com):

“The Camondo family was a prominent European family of Jewish financiers and philanthropists. After the 1497 Spanish decree that ordered the expulsion of all Jews who refused conversion to Catholicism, the Camondo family settled in Venice. There, some of its members became famous by their scholarship and by the services which they rendered to their adopted country. Following the Austrian takeover of Venice in 1798, members of the Camondo family established themselves in Istanbul. Despite the many restrictions imposed on all minorities, the family flourished as merchants in the business section at Galata. They branched into finance in 1802 with the founding of their own bank, Isaac Camondo & Cie. On Isaac’s death in 1832 his brother Abraham Salomon Camondo inherited the bank. He prospered greatly and became the prime banker to the Ottoman Empire until the founding of the Imperial Ottoman Bank in 1863.

In recognition of his contributions and financial assistance to the liberation of Venetia from the Austrian Empire, in 1870 Abraham Salomon Camondo was created a hereditary count by King Victor Emmanuel II of Italy. Abraham died three years later in Paris but in accordance with his wishes his remains were returned to Constantinople for burial there in the Jewish cemetery at Hasköy, a neighborhood on the Golden Horn in Istanbul. His two grandsons remained in Paris and continued to successfully expand their banking business.

This family is now extinct; the last descendants, Nissim de Camondo was killed in aerial combat during World War I in 1917, his father Moïse de Camondo died in 1935, his daughter (and sister of Nissim) Béatrice de Camondo, and her two children Fanny and Bertrand as well as her husband Léon Reinach were deported and murdered in Auschwitz from 1943 to 1945 during World War II.”"