European stock markets closed with mixed results on Tuesday, as oil prices dipped slightly and investors watched for updates on potential progress in U.S.-Iran relations. The FTSE 100, which tracks the performance of the UK’s largest companies, fell 0.3% to 10,708.33, while the FTSE 250, which includes mid-sized British firms, gained 0.1%. The AIM all-share index, which covers smaller companies listed on the London Stock Exchange’s alternative market, also rose slightly. In continental Europe, the Cac 40 in Paris and the Dax 40 in Frankfurt both ended the day with modest gains. In the United States, the Dow Jones Industrial Average declined 0.5% by the time London markets closed, while the S&P 500 remained nearly flat. However, the Nasdaq Composite, which is heavily weighted toward technology stocks, rose 0.4%. Earlier in the week, the Nasdaq reached a record high, fueled by news that Meta Platforms' AI app, Muse, became the most-downloaded free app in the U.S. This boost carried over to Meta's shares, which rose 1.1% on Tuesday, following a strong performance on Monday. A decline in oil prices was supported by hopes for diplomatic progress between the U.S. and Iran. Iran’s President Masoud Pezeshkian is set to attend the United Nations General Assembly in New York, and investors are watching for any potential meetings with former U.S. President Donald Trump. Reports suggest Iran might consider reopening the Strait of Hormuz, a critical oil shipping route, within seven days if U.S. military pressure is reduced. These developments were initially reported by Japan’s Kyoto News and are seen as a possible step toward ending hostilities between the two nations. Brent crude oil, a global benchmark for oil prices, fell to $99.39 a barrel on Tuesday, down from $100.28 the previous day. U.S. Treasury yields, which influence borrowing costs for governments and businesses, remained largely unchanged. The British pound weakened slightly against the U.S. dollar but gained a small edge against the euro. In the UK, public sector borrowing exceeded expectations in August, reaching £18.27 billion, up from £15.35 billion in the same period last year and higher than the forecast of £15.7 billion. On the FTSE 100, Kingfisher and Smiths Group saw strong gains after reporting positive earnings. Kingfisher, a major UK DIY retailer, rose 12% after its Screwfix brand outperformed expectations and the company raised its full-year profit forecast. Smiths Group climbed 7.5% despite a drop in annual profit, as it announced a new share buyback. Other notable risers included JD Sports Fashion and International Consolidated Airlines, the latter benefiting from lower oil prices. Conversely, defense firms BAE Systems and Babcock International fell due to expectations of reduced military activity in the Middle East and Ukraine. Standard Chartered, an Asia-focused bank, dropped 2.3% after it was found to have processed billions for a Russian-linked financial network using forged documents.