{"paper":{"title":"Maximal area integral problem for certain class of univalent analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Navneet Lal Sharma, Saminathan Ponnusamy, Swadesh Kumar Sahoo","submitted_at":"2014-07-21T11:02:02Z","abstract_excerpt":"One of the classical problems concerns the class of analytic functions $f$ on the open unit disk $|z|<1$ which have finite Dirichlet integral $\\Delta(1,f)$, where $$\\Delta(r,f)=\\iint_{|z|<r}|f'(z)|^2 \\, dxdy \\quad (0<r\\leq 1). $$ The class ${\\mathcal S}^*(A,B)$ of normalized functions $f$ analytic in $|z|<1$ and satisfies the subordination condition $zf'(z)/f(z)\\prec (1+Az)/(1+Bz)$ in $|z|<1$ and for some $-1\\leq B\\leq 0$, $A\\in {\\mathbb C}$ with $A\\neq B$, has been studied extensively. In this paper, we solve the extremal problem of determining the value of $$\\max_{f\\in {\\mathcal S}^*(A,B)}\\D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5454","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"}