A constructive proof of the infinite version of the Belluce-Kirk theorem

Name: Work Video:
Duration: 3 min 30 s
Description: In [5], we proved the following infinite version of the Bellucekirk theorem [1]:THEOREM 1 [5].Let K be a nonempty weakly compact convex subset of a Banach space and assume that K possesses normal structure.Let F be a commutative family of nonexpansive selfmappings of K. Then J^ has a common fixed point.
Teck Cheong Lim
{'id': 'https://openalex.org/W2018846527', 'doi': 'https://doi.org/10.2140/pjm.1979.81.467', 'title': 'A constructive proof of the infinite version of the Belluce-Kirk theorem', 'display_name': 'A constructive proof of the infinite version of the Belluce-Kirk theorem', 'publication_year': 1979, 'publication_date': '1979-04-01', 'ids': {'openalex': 'https://openalex.org/W2018846527', 'doi': 'https://doi.org/10.2140/pjm.1979.81.467', 'mag': '2018846527'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.2140/pjm.1979.81.467', 'pdf_url': 'http://msp.org/pjm/1979/81-2/pjm-v81-n2-p14-s.pdf', 'source': {'id': 'https://openalex.org/S130774151', 'display_name': 'Pacific Journal of Mathematics', 'issn_l': '0030-8730', 'issn': ['0030-8730', '1945-5844'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'http://msp.org/pjm/1979/81-2/pjm-v81-n2-p14-s.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5110026902', 'display_name': 'Teck Cheong Lim', 'orcid': None}, 'institutions': [], 'countries': ['JP'], 'is_corresponding': True, 'raw_author_name': 'Teck Cheong Lim', 'raw_affiliation_strings': ['8-8, 3-chome, Takadanobaba, Shinjuku-ku, Tokyo 160, Japan.'], 'affiliations': [{'raw_affiliation_string': '8-8, 3-chome, Takadanobaba, Shinjuku-ku, Tokyo 160, Japan.', 'institution_ids': []}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5110026902'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 14.055, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 26, 'citation_normalized_percentile': {'value': 0.402796, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 89, 'max': 90}, 'biblio': {'volume': '81', 'issue': '2', 'first_page': '467', 'last_page': '469'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10545', 'display_name': 'Optimization and Variational Analysis', 'score': 0.9888, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10545', 'display_name': 'Optimization and Variational Analysis', 'score': 0.9888, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T12508', 'display_name': 'Functional Equations Stability Results', 'score': 0.9852, '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/T10046', 'display_name': 'Stability and Control of Uncertain Systems', 'score': 0.9772, 'subfield': {'id': 'https://openalex.org/subfields/2207', 'display_name': 'Control and Systems Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/constructive', 'display_name': 'Constructive', 'score': 0.6403998}, {'id': 'https://openalex.org/keywords/constructive-proof', 'display_name': 'Constructive proof', 'score': 0.48312733}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8485601}, {'id': 'https://openalex.org/C45962547', 'wikidata': 'https://www.wikidata.org/wiki/Q1422068', 'display_name': 'Fixed-point theorem', 'level': 2, 'score': 0.7336781}, {'id': 'https://openalex.org/C2778701210', 'wikidata': 'https://www.wikidata.org/wiki/Q28130034', 'display_name': 'Constructive', 'level': 3, 'score': 0.6403998}, {'id': 'https://openalex.org/C167729594', 'wikidata': 'https://www.wikidata.org/wiki/Q17736', 'display_name': 'Axiom', 'level': 2, 'score': 0.6236773}, {'id': 'https://openalex.org/C194886279', 'wikidata': 'https://www.wikidata.org/wiki/Q430271', 'display_name': 'Fundamental theorem', 'level': 3, 'score': 0.57711744}, {'id': 'https://openalex.org/C206929604', 'wikidata': 'https://www.wikidata.org/wiki/Q530152', 'display_name': 'Picard–Lindelöf theorem', 'level': 3, 'score': 0.56252176}, {'id': 'https://openalex.org/C146147875', 'wikidata': 'https://www.wikidata.org/wiki/Q1144897', 'display_name': 'Brouwer fixed-point theorem', 'level': 3, 'score': 0.54693145}, {'id': 'https://openalex.org/C151797676', 'wikidata': 'https://www.wikidata.org/wiki/Q179692', 'display_name': 'Axiom of choice', 'level': 4, 'score': 0.5181421}, {'id': 'https://openalex.org/C48540410', 'wikidata': 'https://www.wikidata.org/wiki/Q5221089', 'display_name': "Danskin's theorem", 'level': 4, 'score': 0.5019183}, {'id': 'https://openalex.org/C171636804', 'wikidata': 'https://www.wikidata.org/wiki/Q1149458', 'display_name': 'Compactness theorem', 'level': 4, 'score': 0.4969974}, {'id': 'https://openalex.org/C202854965', 'wikidata': 'https://www.wikidata.org/wiki/Q3044470', 'display_name': 'Constructive proof', 'level': 2, 'score': 0.48312733}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.4655498}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.40780294}, {'id': 'https://openalex.org/C2777686260', 'wikidata': 'https://www.wikidata.org/wiki/Q144037', 'display_name': 'Calculus (dental)', 'level': 2, 'score': 0.3925424}, {'id': 'https://openalex.org/C144237770', 'wikidata': 'https://www.wikidata.org/wiki/Q747534', 'display_name': 'Mathematical economics', 'level': 1, 'score': 0.33541355}, {'id': 'https://openalex.org/C153046414', 'wikidata': 'https://www.wikidata.org/wiki/Q12482', 'display_name': 'Set theory', 'level': 3, 'score': 0.19219384}, {'id': 'https://openalex.org/C177264268', 'wikidata': 'https://www.wikidata.org/wiki/Q1514741', 'display_name': 'Set (abstract data type)', 'level': 2, 'score': 0.10171345}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.06691137}, {'id': 'https://openalex.org/C71924100', 'wikidata': 'https://www.wikidata.org/wiki/Q11190', 'display_name': 'Medicine', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C98045186', 'wikidata': 'https://www.wikidata.org/wiki/Q205663', 'display_name': 'Process (computing)', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C199343813', 'wikidata': 'https://www.wikidata.org/wiki/Q12128', 'display_name': 'Dentistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C111919701', 'wikidata': 'https://www.wikidata.org/wiki/Q9135', 'display_name': 'Operating system', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.2140/pjm.1979.81.467', 'pdf_url': 'http://msp.org/pjm/1979/81-2/pjm-v81-n2-p14-s.pdf', 'source': {'id': 'https://openalex.org/S130774151', 'display_name': 'Pacific Journal of Mathematics', 'issn_l': '0030-8730', 'issn': ['0030-8730', '1945-5844'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'http://projecteuclid.org/euclid.pjm/1102785287', 'pdf_url': 'https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-81/issue-2/A-constructive-proof-of-the-infinite-version-of-the-Belluce/pjm/1102785287.pdf', 'source': {'id': 'https://openalex.org/S4306400787', 'display_name': 'Project Euclid (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.2140/pjm.1979.81.467', 'pdf_url': 'http://msp.org/pjm/1979/81-2/pjm-v81-n2-p14-s.pdf', 'source': {'id': 'https://openalex.org/S130774151', 'display_name': 'Pacific Journal of Mathematics', 'issn_l': '0030-8730', 'issn': ['0030-8730', '1945-5844'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 29, 'referenced_works': ['https://openalex.org/W1504714386', 'https://openalex.org/W1965156515', 'https://openalex.org/W1970491240', 'https://openalex.org/W1983735941', 'https://openalex.org/W1985132925', 'https://openalex.org/W1991199099', 'https://openalex.org/W2006696115', 'https://openalex.org/W2016594683', 'https://openalex.org/W2018297437', 'https://openalex.org/W2018846527', 'https://openalex.org/W2029605071', 'https://openalex.org/W2032296189', 'https://openalex.org/W2033937564', 'https://openalex.org/W2035025075', 'https://openalex.org/W2035725761', 'https://openalex.org/W2035774218', 'https://openalex.org/W2037108626', 'https://openalex.org/W2038210820', 'https://openalex.org/W2038262440', 'https://openalex.org/W2040432725', 'https://openalex.org/W2045656867', 'https://openalex.org/W2046917065', 'https://openalex.org/W2072898517', 'https://openalex.org/W2081953823', 'https://openalex.org/W2085002500', 'https://openalex.org/W2128723198', 'https://openalex.org/W2150503759', 'https://openalex.org/W2160978372', 'https://openalex.org/W4251025106'], 'related_works': ['https://openalex.org/W2492532462', 'https://openalex.org/W2393711911', 'https://openalex.org/W2366068903', 'https://openalex.org/W2359037450', 'https://openalex.org/W2357396962', 'https://openalex.org/W2353439471', 'https://openalex.org/W2063265350', 'https://openalex.org/W2044132465', 'https://openalex.org/W2029256996', 'https://openalex.org/W1977021713'], 'abstract_inverted_index': {'In': [0], '[5],': [1], 'we': [2], 'proved': [3], 'the': [4, 9], 'following': [5], 'infinite': [6], 'version': [7], 'of': [8, 23, 39, 42], 'Bellucekirk': [10], 'theorem': [11], '[1]:THEOREM': [12], '1': [13], '[5].Let': [14], 'K': [15, 30], 'be': [16, 35], 'a': [17, 24, 36, 47], 'nonempty': [18], 'weakly': [19], 'compact': [20], 'convex': [21], 'subset': [22], 'Banach': [25], 'space': [26], 'and': [27], 'assume': [28], 'that': [29], 'possesses': [31], 'normal': [32], 'structure.Let': [33], 'F': [34], 'commutative': [37], 'family': [38], 'nonexpansive': [40], 'selfmappings': [41], 'K.': [43], 'Then': [44], 'J^': [45], 'has': [46], 'common': [48], 'fixed': [49], 'point.': [50]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2018846527', 'counts_by_year': [], 'updated_date': '2024-12-13T19:58:19.030786', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
