{"paper":{"title":"Generalized variational inclusion governed by generalized $\\alpha\\beta$-$H((., .), (., .))$-mixed accretive mapping in real $q$-uniformly smooth Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sanjeev Gupta, Shamshad Husain, Vishnu Narayan Mishra","submitted_at":"2015-09-06T14:34:25Z","abstract_excerpt":"In this paper, we investigate a new notion of accretive mappings called generalized $\\alpha\\beta$-$H((.,.),(.,.))$-mixed accretive mappings in Banach spaces. We extend the concept of proximal-point mappings associated with generalized $m$-accretive mappings to the generalized $\\alpha\\beta$-$H((.,.),(.,.))$-mixed accretive mappings and prove that the proximal-point mapping associated with generalized $\\alpha\\beta$-$H((.,.),(.,.))$-mixed accretive mapping is single-valued and Lipschitz continuous. Some examples are given to justify the definition of generalized $\\alpha\\beta$-$H((.,.),(.,.))$-mix"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01601","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":""},"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"}