Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W3190629980', 'doi': 'https://doi.org/10.1007/bf01830975', 'title': 'Approximate homomorphisms', 'display_name': 'Approximate homomorphisms', 'publication_year': 1992, 'publication_date': '1992-10-01', 'ids': {'openalex': 'https://openalex.org/W3190629980', 'doi': 'https://doi.org/10.1007/bf01830975', 'mag': '3190629980'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/bf01830975', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S150892397', 'display_name': 'Aequationes Mathematicae', 'issn_l': '0001-9054', 'issn': ['0001-9054', '1420-8903'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320186', 'host_organization_name': 'Birkhäuser', 'host_organization_lineage': ['https://openalex.org/P4310320186', 'https://openalex.org/P4310319900', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Birkhäuser', 'Springer Science+Business Media', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5060026505', 'display_name': 'D. H. Hyers', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I1174212', 'display_name': 'University of Southern California', 'ror': 'https://ror.org/03taz7m60', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I1174212']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Donald H. Hyers', 'raw_affiliation_strings': ['Department of Mathematics, University of Southern California, 90089-1113, Los Angeles, California, USA'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, University of Southern California, 90089-1113, Los Angeles, California, USA', 'institution_ids': ['https://openalex.org/I1174212']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5065451895', 'display_name': 'Themistocles M. Rassias', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I1174212', 'display_name': 'University of Southern California', 'ror': 'https://ror.org/03taz7m60', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I1174212']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Themistocles M. Rassias', 'raw_affiliation_strings': ['Department of Mathematics, University of Southern California, 90089-1113, Los Angeles, California, USA'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, University of Southern California, 90089-1113, Los Angeles, California, USA', 'institution_ids': ['https://openalex.org/I1174212']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 2190, 'currency': 'EUR', 'value_usd': 2790, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 3.741, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 532, 'citation_normalized_percentile': {'value': 0.986068, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 99, 'max': 100}, 'biblio': {'volume': '44', 'issue': '2-3', 'first_page': '125', 'last_page': '153'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12508', 'display_name': 'Stability of Functional Equations in Mathematical Analysis', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T12508', 'display_name': 'Stability of Functional Equations in Mathematical Analysis', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T13400', 'display_name': 'Applications of Generalized Functions in Mathematics and Physics', 'score': 0.963, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/section', 'display_name': 'Section (typography)', 'score': 0.6235967}, {'id': 'https://openalex.org/keywords/approximate-homomorphisms', 'display_name': 'Approximate Homomorphisms', 'score': 0.581998}, {'id': 'https://openalex.org/keywords/subring', 'display_name': 'Subring', 'score': 0.52418894}, {'id': 'https://openalex.org/keywords/hyers-ulam-stability', 'display_name': 'Hyers-Ulam Stability', 'score': 0.514303}, {'id': 'https://openalex.org/keywords/banach-spaces', 'display_name': 'Banach Spaces', 'score': 0.504333}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.9086327}, {'id': 'https://openalex.org/C136170076', 'wikidata': 'https://www.wikidata.org/wiki/Q181296', 'display_name': 'Abelian group', 'level': 2, 'score': 0.7108679}, {'id': 'https://openalex.org/C2780129039', 'wikidata': 'https://www.wikidata.org/wiki/Q1931107', 'display_name': 'Section (typography)', 'level': 2, 'score': 0.6235967}, {'id': 'https://openalex.org/C42747912', 'wikidata': 'https://www.wikidata.org/wiki/Q1048447', 'display_name': 'Multiplicative function', 'level': 2, 'score': 0.5762078}, {'id': 'https://openalex.org/C4042151', 'wikidata': 'https://www.wikidata.org/wiki/Q215111', 'display_name': 'Homomorphism', 'level': 2, 'score': 0.5301137}, {'id': 'https://openalex.org/C132954091', 'wikidata': 'https://www.wikidata.org/wiki/Q194397', 'display_name': 'Banach space', 'level': 2, 'score': 0.5284132}, {'id': 'https://openalex.org/C21714298', 'wikidata': 'https://www.wikidata.org/wiki/Q929536', 'display_name': 'Subring', 'level': 3, 'score': 0.52418894}, {'id': 'https://openalex.org/C183778304', 'wikidata': 'https://www.wikidata.org/wiki/Q165474', 'display_name': 'Commutative property', 'level': 2, 'score': 0.52139765}, {'id': 'https://openalex.org/C31498916', 'wikidata': 'https://www.wikidata.org/wiki/Q583034', 'display_name': 'Locally compact space', 'level': 2, 'score': 0.44825172}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.4284305}, {'id': 'https://openalex.org/C207405024', 'wikidata': 'https://www.wikidata.org/wiki/Q207348', 'display_name': 'Semigroup', 'level': 2, 'score': 0.42702776}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.41150483}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.3325777}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.13354346}, {'id': 'https://openalex.org/C2780378348', 'wikidata': 'https://www.wikidata.org/wiki/Q25351438', 'display_name': 'Ring (chemistry)', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C178790620', 'wikidata': 'https://www.wikidata.org/wiki/Q11351', 'display_name': 'Organic chemistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C112698675', 'wikidata': 'https://www.wikidata.org/wiki/Q37038', 'display_name': 'Advertising', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C144133560', 'wikidata': 'https://www.wikidata.org/wiki/Q4830453', 'display_name': 'Business', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/bf01830975', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S150892397', 'display_name': 'Aequationes Mathematicae', 'issn_l': '0001-9054', 'issn': ['0001-9054', '1420-8903'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320186', 'host_organization_name': 'Birkhäuser', 'host_organization_lineage': ['https://openalex.org/P4310320186', 'https://openalex.org/P4310319900', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Birkhäuser', 'Springer Science+Business Media', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 41, 'referenced_works': ['https://openalex.org/W1041314902', 'https://openalex.org/W1044527965', 'https://openalex.org/W1531724333', 'https://openalex.org/W1533006072', 'https://openalex.org/W1571664348', 'https://openalex.org/W1617264149', 'https://openalex.org/W175230274', 'https://openalex.org/W1963881509', 'https://openalex.org/W1980306557', 'https://openalex.org/W1987702649', 'https://openalex.org/W1988486889', 'https://openalex.org/W1993173981', 'https://openalex.org/W1998033412', 'https://openalex.org/W2003874621', 'https://openalex.org/W2010297701', 'https://openalex.org/W2021139948', 'https://openalex.org/W202438975', 'https://openalex.org/W2027339522', 'https://openalex.org/W2028185219', 'https://openalex.org/W2030341413', 'https://openalex.org/W2042526402', 'https://openalex.org/W2046465850', 'https://openalex.org/W2052079226', 'https://openalex.org/W2053355731', 'https://openalex.org/W2055155612', 'https://openalex.org/W2059593678', 'https://openalex.org/W2060594912', 'https://openalex.org/W2064402345', 'https://openalex.org/W2083971740', 'https://openalex.org/W2089423756', 'https://openalex.org/W2319149694', 'https://openalex.org/W2319308948', 'https://openalex.org/W2328784069', 'https://openalex.org/W269720352', 'https://openalex.org/W298315413', 'https://openalex.org/W4210945509', 'https://openalex.org/W4211258748', 'https://openalex.org/W4230786268', 'https://openalex.org/W4248217835', 'https://openalex.org/W4313159870', 'https://openalex.org/W817595593'], 'related_works': ['https://openalex.org/W4306684106', 'https://openalex.org/W4242719885', 'https://openalex.org/W3153960211', 'https://openalex.org/W3083299250', 'https://openalex.org/W2755430855', 'https://openalex.org/W2390566315', 'https://openalex.org/W2360714468', 'https://openalex.org/W2160742401', 'https://openalex.org/W2127477595', 'https://openalex.org/W1478387340'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3190629980', 'counts_by_year': [{'year': 2024, 'cited_by_count': 13}, {'year': 2023, 'cited_by_count': 9}, {'year': 2022, 'cited_by_count': 6}, {'year': 2021, 'cited_by_count': 14}, {'year': 2020, 'cited_by_count': 4}, {'year': 2019, 'cited_by_count': 7}, {'year': 2018, 'cited_by_count': 13}, {'year': 2017, 'cited_by_count': 8}, {'year': 2016, 'cited_by_count': 15}, {'year': 2015, 'cited_by_count': 23}, {'year': 2014, 'cited_by_count': 24}, {'year': 2013, 'cited_by_count': 25}, {'year': 2012, 'cited_by_count': 55}], 'updated_date': '2024-09-10T14:51:02.692229', 'created_date': '2021-08-16'}