HSBC Holdings Plc is aiming to challenge India’s private-sector banks, betting that the country’s swelling pool of affluent customers and globally connected citizens can fuel its next phase of growth as it pushes deeper into smaller cities. The London-based lender is doubling down in the world’s fastest-growing major economy across three areas — wealth, transaction banking and what Hitendra Dave, HSBC’s India chief executive officer, calls “globality,” - using its international network to cater to clients whose businesses and wealth span borders.