{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:F7PNZXSR643KGOOJOCD7J5E3GL","short_pith_number":"pith:F7PNZXSR","canonical_record":{"source":{"id":"2209.13200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-09-27T07:01:00Z","cross_cats_sorted":[],"title_canon_sha256":"11b2362ca57569bc273c5a2b4fd850a33ea33731a3480b64c87d12b730129d30","abstract_canon_sha256":"59b9815b8c5c6ab10f00a28ea1dd3667cf14002c30931801f64eebdff54f6b1c"},"schema_version":"1.0"},"canonical_sha256":"2fdedcde51f736a339c97087f4f49b32db610fa467fadaa0c9e1fda0a4f075f4","source":{"kind":"arxiv","id":"2209.13200","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.13200","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"arxiv_version","alias_value":"2209.13200v1","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.13200","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_12","alias_value":"F7PNZXSR643K","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_16","alias_value":"F7PNZXSR643KGOOJ","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_8","alias_value":"F7PNZXSR","created_at":"2026-07-05T05:01:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:F7PNZXSR643KGOOJOCD7J5E3GL","target":"record","payload":{"canonical_record":{"source":{"id":"2209.13200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-09-27T07:01:00Z","cross_cats_sorted":[],"title_canon_sha256":"11b2362ca57569bc273c5a2b4fd850a33ea33731a3480b64c87d12b730129d30","abstract_canon_sha256":"59b9815b8c5c6ab10f00a28ea1dd3667cf14002c30931801f64eebdff54f6b1c"},"schema_version":"1.0"},"canonical_sha256":"2fdedcde51f736a339c97087f4f49b32db610fa467fadaa0c9e1fda0a4f075f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:01:07.660168Z","signature_b64":"7P8LHGnGMZSbKHNqvjjz3rJxloP/+0pQTCoUHXYvqNq7XeJf+hGJIzPPbyeDhoglbUybZYlE95W+bzFhHsaSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fdedcde51f736a339c97087f4f49b32db610fa467fadaa0c9e1fda0a4f075f4","last_reissued_at":"2026-07-05T05:01:07.659835Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:01:07.659835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.13200","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:01:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cW0FTeeCFYT+K9q4iuub5DbVP+PJAw558VWfI6NZxv9EruvUqqT/PdF4iK0gv6wTVjs1pXACg1vxo8RQE3jUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T02:57:01.506102Z"},"content_sha256":"0d9aebb9f7e61b59c91d1e95fcf2401114ed844e3f2a16d6945decb21b440a90","schema_version":"1.0","event_id":"sha256:0d9aebb9f7e61b59c91d1e95fcf2401114ed844e3f2a16d6945decb21b440a90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:F7PNZXSR643KGOOJOCD7J5E3GL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed point results of enriched interpolative Kannan type operators with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mujahid Abbas, Rizwan Anjum, Shakeela Riasat","submitted_at":"2022-09-27T07:01:00Z","abstract_excerpt":"The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains the classes of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskii iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.13200","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.13200/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:01:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXDDqtQdCBb0RYtt8Y+DtultFiwGI7QdRRdaw0/cvH7pcODrVQ6ByGewfYAmXUs85+V6IenqwqdAE6waUfmnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T02:57:01.506480Z"},"content_sha256":"e85a962b6452df96be5aa90626264055feea556e092672f59cba50e0dcaccf78","schema_version":"1.0","event_id":"sha256:e85a962b6452df96be5aa90626264055feea556e092672f59cba50e0dcaccf78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F7PNZXSR643KGOOJOCD7J5E3GL/bundle.json","state_url":"https://pith.science/pith/F7PNZXSR643KGOOJOCD7J5E3GL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F7PNZXSR643KGOOJOCD7J5E3GL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-22T02:57:01Z","links":{"resolver":"https://pith.science/pith/F7PNZXSR643KGOOJOCD7J5E3GL","bundle":"https://pith.science/pith/F7PNZXSR643KGOOJOCD7J5E3GL/bundle.json","state":"https://pith.science/pith/F7PNZXSR643KGOOJOCD7J5E3GL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F7PNZXSR643KGOOJOCD7J5E3GL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:F7PNZXSR643KGOOJOCD7J5E3GL","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":"59b9815b8c5c6ab10f00a28ea1dd3667cf14002c30931801f64eebdff54f6b1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-09-27T07:01:00Z","title_canon_sha256":"11b2362ca57569bc273c5a2b4fd850a33ea33731a3480b64c87d12b730129d30"},"schema_version":"1.0","source":{"id":"2209.13200","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.13200","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"arxiv_version","alias_value":"2209.13200v1","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.13200","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_12","alias_value":"F7PNZXSR643K","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_16","alias_value":"F7PNZXSR643KGOOJ","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_8","alias_value":"F7PNZXSR","created_at":"2026-07-05T05:01:07Z"}],"graph_snapshots":[{"event_id":"sha256:e85a962b6452df96be5aa90626264055feea556e092672f59cba50e0dcaccf78","target":"graph","created_at":"2026-07-05T05:01:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.13200/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains the classes of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskii iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an","authors_text":"Mujahid Abbas, Rizwan Anjum, Shakeela Riasat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-09-27T07:01:00Z","title":"Fixed point results of enriched interpolative Kannan type operators with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.13200","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":"sha256:0d9aebb9f7e61b59c91d1e95fcf2401114ed844e3f2a16d6945decb21b440a90","target":"record","created_at":"2026-07-05T05:01:07Z","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":"59b9815b8c5c6ab10f00a28ea1dd3667cf14002c30931801f64eebdff54f6b1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-09-27T07:01:00Z","title_canon_sha256":"11b2362ca57569bc273c5a2b4fd850a33ea33731a3480b64c87d12b730129d30"},"schema_version":"1.0","source":{"id":"2209.13200","kind":"arxiv","version":1}},"canonical_sha256":"2fdedcde51f736a339c97087f4f49b32db610fa467fadaa0c9e1fda0a4f075f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fdedcde51f736a339c97087f4f49b32db610fa467fadaa0c9e1fda0a4f075f4","first_computed_at":"2026-07-05T05:01:07.659835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:01:07.659835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7P8LHGnGMZSbKHNqvjjz3rJxloP/+0pQTCoUHXYvqNq7XeJf+hGJIzPPbyeDhoglbUybZYlE95W+bzFhHsaSAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:01:07.660168Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.13200","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d9aebb9f7e61b59c91d1e95fcf2401114ed844e3f2a16d6945decb21b440a90","sha256:e85a962b6452df96be5aa90626264055feea556e092672f59cba50e0dcaccf78"],"state_sha256":"767885187c782e96c50a8243a39659a0e40ba6ff576c706aa11d861c071e1c7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uafXmhpnzyDdkeyGwWwFbXFnFa/R3Vsitp8gxuCHvN66ZA6W1MAQodOoWsD269N7lj2ddDdR36SiuGqBUEayBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-22T02:57:01.508534Z","bundle_sha256":"56fe2ab9c78a68bddeecd8cbd90ecb0cc5233db3866e5349e18d5d2b2ba81848"}}