{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JSJYH3L7ESJNDCX5CULDL365RL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d57d2f72fc23bf10c25022c7216555dea6ad7f4de32298620e4fad3c543287b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-22T21:07:36Z","title_canon_sha256":"5b8478b3569fa57e5d6e3b1d58e57f7ffc8ba8eb5d11349f03ac42c7890bb8ab"},"schema_version":"1.0","source":{"id":"1609.07163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07163","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07163v1","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07163","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"JSJYH3L7ESJN","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JSJYH3L7ESJNDCX5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JSJYH3L7","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:dc0d0ae320a156e53d13551281dbb4efaccf647de85e94af6137c4e945b07fef","target":"graph","created_at":"2026-05-18T01:04:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Mean nonexpansive mappings were first introduced in 2007 by Goebel and Japon Pineda and advances have been made by several authors toward understanding their fixed point properties in various contexts. For any given $(\\alpha_1, \\alpha_2)$-nonexpansive mapping $T$ of a Banach space, many of the positive results have been derived from properties of the mapping $T_\\alpha = \\alpha_1 T + \\alpha_2T^2= (\\alpha_1I + \\alpha_2T)\\circ T$ which is nonexpansive. However, the related mapping $T \\circ (\\alpha_1I + \\alpha_2T)$ has not yet been studied. In this paper, we investigate some fixed point properties","authors_text":"Torrey M. Gallagher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-22T21:07:36Z","title":"Fixed point results for a new mapping related to mean nonexpansive mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07163","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5819dfd1df9a9c1ffd314b66d7e88808b4c8a4dbab16fe20c1a873afae0f011f","target":"record","created_at":"2026-05-18T01:04:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d57d2f72fc23bf10c25022c7216555dea6ad7f4de32298620e4fad3c543287b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-22T21:07:36Z","title_canon_sha256":"5b8478b3569fa57e5d6e3b1d58e57f7ffc8ba8eb5d11349f03ac42c7890bb8ab"},"schema_version":"1.0","source":{"id":"1609.07163","kind":"arxiv","version":1}},"canonical_sha256":"4c9383ed7f2492d18afd151635efdd8ac23868f2d60058698d816a1cc4d08cef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c9383ed7f2492d18afd151635efdd8ac23868f2d60058698d816a1cc4d08cef","first_computed_at":"2026-05-18T01:04:02.106294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:02.106294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rFm+51B1+1E3YS+Tiv85h6dm2/rwSYN9mRHvCMs8QJIHKoXqStX0nS8xq3wiIMmaqvT7cVR6+kB5mogFXkSJBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:02.107010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5819dfd1df9a9c1ffd314b66d7e88808b4c8a4dbab16fe20c1a873afae0f011f","sha256:dc0d0ae320a156e53d13551281dbb4efaccf647de85e94af6137c4e945b07fef"],"state_sha256":"0a6088bdba6c880cec96a186b234672355c8a81709a20d79e0a3a85e9908a6f5"}