{'fraction_non_alphanumeric': 0.045816733067729085, 'fraction_numerical': 0.0, 'mean_word_length': 5.367088607594937, '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}}
Mathematical programming involving B-(Hp,r,α)-generalized convex functions

In this paper, we introduce new types of generalized convex functions including locally B-(Hp, r, α)-preinvex functions and B̄(Hp, r, α)-invex functions based on Hp-invex set. Some properties of these new classes of functions and sets are established. We also present the optimality conditions for mathematical programming problems in which the functions considered belong to the classes of functions introduced in this paper.