{'fraction_non_alphanumeric': 0.01507537688442211, 'fraction_numerical': 0.0, 'mean_word_length': 5.1020408163265305, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Existence of Fixed Points for a Class of Decreasing Operators with Parameter and Applications

This paper studies the existence of fixed points for a class of decreasing operators with parameter in real Banach spaces. The existence theorems of fixed point are obtained as when the parameter is increasing, there will still be a large fixed point. These results have reduced the requirements of convexity, compactness, and lattice structure of spaces. By this new method, the existence of solutions for a class of second-order differential equations with parameter in infinite intervals is studied.