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HYERS-ULAM STABILITY OF A CLOSED OPERATOR IN A HILBERT SPACE
Hirasawa Go,Miura Takeshi Korean Mathematical Society 2006 대한수학회보 Vol.43 No.1
We give some necessary and sufficient conditions in order that a closed operator in a Hilbert space into another have the Hyers-Ulam stability. Moreover, we prove the existence of the stability constant for a closed operator. We also determine the stability constant in terms of the lower bound.
A perturbation of ring derivations on Banach algebras
Miura, Takeshi,Hirasawa, Go,Takahasi, Sin-Ei Elsevier 2006 Journal of mathematical analysis and applications Vol.319 No.2
<P><B>Abstract</B></P><P>Suppose <I>A</I> is a Banach algebra and suppose f:A→A is an approximate ring derivation in the sense of Hyers–Ulam–Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297–300]. If <I>A</I> has an approximate identity, or if <I>A</I> is semisimple and commutative, then we prove that <I>f</I> is an exact ring derivation.</P>
Hyers-Ulam stability of a closed operator in a Hilbert space
Go Hirasawa,Takeshi Miura 대한수학회 2006 대한수학회보 Vol.43 No.1
sufficient conditions in order that a closed operator in a Hilbertspace into another have the Hyers-Ulam stability. Moreover, weprove the existence of the stability constant for a closedoperator. We also determine the stability constant in terms of the lower bound.
Wataru Yamagami,Nobuyuki Susumu,Takeshi Makabe,Kensuke Sakai,Hiroyuki Nomura,Fumio Kataoka,Akira Hirasawa,Kouji Banno,Daisuke Aoki 대한부인종양학회 2018 Journal of Gynecologic Oncology Vol.29 No.2
Objective: Reports on the repeated administration of medroxyprogesterone acetate (MPA) for intrauterine recurrence after fertility-preserving therapy for atypical endometrial hyperplasia (AEH) and early grade 1 endometrioid carcinoma (G1) are lacking. We aimed to clarify the outcomes of repeated MPA therapy in cases of intrauterine recurrence after fertility-preserving therapy with MPA against AEH/early G1. Methods: Patients with AEH or stage IA well-differentiated endometrioid carcinoma without myometrial invasion who underwent first-line MPA therapy for primary lesions or intrauterine recurrence were divided into initial treatment and repeated treatment groups (162 and 82 patients, respectively). Oral MPA administration (400−600 mg/day) was continued until pathological tumor disappearance. Data regarding clinicopathological factors, adverse events, and outcomes following the initial and repeated hormonal treatments were extracted from medical records and analyzed. Results: Complete response rates in the initial and repeated treatment groups were 98.5% and 96.4%, respectively, among patients with AEH, and were 90.7% and 98.1%, respectively, among patients with G1. In the initial treatment group, 5-year recurrence-free survival (RFS) rates were 53.7% and 33.2% among patients with AEH and G1, respectively. In the repeated treatment group, RFS rates were 14.0% and 11.2% among patients with AEH and G1, respectively. Among patients with AEH, the pregnancy rate tended to be lower in the repeated treatment group than in the initial treatment group (11.1% vs. 29.2%; p=0.107), while no significant group difference was observed among patients with G1 (20.8% vs. 22.7%). Conclusion: Repeated treatment is sufficiently effective for intrauterine recurrence after hormonal therapy for AEH/early G1.
Aikou Okamoto,Eiji Kondo,Toshiaki Nakamura,Satoshi Yanagida,Junzo Hamanishi,Kenichi Harano,Kosei Hasegawa,Takeshi Hirasawa,Kensuke Hori,Shinichi Komiyama,Motoki Matsuura,Hidekatsu Nakai,Hiroko Nakamur 대한부인종양학회 2021 Journal of Gynecologic Oncology Vol.32 No.2
Objective: To evaluate the efficacy and safety of niraparib in Japanese women with heavilypretreated ovarian cancer. Methods: This Phase 2 open-label, single-arm study enrolled Japanese women withhomologous recombination deficiency-positive relapsed, high-grade serous ovarian,fallopian tube, or primary peritoneal cancer who had completed 3–4 lines of therapy. The starting dose of niraparib was 300 mg administered once daily in continuous 28-daycycles until objective progressive disease, unacceptable toxicity, consent withdrawal ordiscontinuation. The primary endpoint, objective response rate (ORR), was assessed bythe investigator using RECIST version 1.1. Safety evaluations included the incidence oftreatment-emergent adverse events (TEAEs), including serious TEAEs. Results: Twenty women were enrolled and the confirmed ORR in the full analysis set (FAS)was 35.0% (7/20), consisting of 1 complete response and 6 partial responses. Diseasecontrol rate in the FAS was 90.0%. The most frequently reported TEAEs (>50%) wereanemia, nausea, and platelet count decreased. One patient (5.0%) had TEAEs leadingto discontinuation of niraparib whereas reductions or interruptions were reported in 14(70.0%) and 15 (75.0%) patients, respectively. The median dose intensity (202.9 mg daily)corresponded to a relative dose intensity of 67.6%. Conclusion: Efficacy and safety of niraparib in heavily pretreated Japanese women wascomparable to that seen in an equivalent population of non-Japanese women. No new safetysignals were identified.Trial Registration: ClinicalTrials.gov Identifier: NCT03759600
Daisuke Aoki,Aikou Okamoto,Tsutomu Tabata,Satoshi Yanagida,Toshiaki Nakamura,Eiji Kondo,Junzo Hamanishi,Kenichi Harano,Kosei Hasegawa,Takeshi Hirasawa,Kensuke Hori 대한부인종양학회 2024 Journal of Gynecologic Oncology Vol.35 No.5
Objective: This study evaluated the long-term safety and efficacy of niraparib in Japanese patients with platinum-sensitive recurrent ovarian cancer. Methods: This was a follow-up analysis of a phase 2, multicenter, open-label, single-arm study in Japanese women with platinum-sensitive, relapsed ovarian cancer. Participants received niraparib (starting dose 300 mg) once daily in continuous 28-day cycles. The primary endpoint was the incidence of Grade 3 or 4 thrombocytopenia-related events (defined as the overall incidence of the MedDRA Preferred Terms “thrombocytopenia” and “platelet count decreased”) occurring in the 30 days after initial administration of niraparib, and secondary endpoints included evaluation of treatment-emergent adverse events and progression-free survival. Results: Nineteen patients (median age, 62 years; median body weight, 53.9 kg) were enrolled. As previously reported, the incidence of Grade 3 or 4 thrombocytopenia-related events during the first 30 days of treatment was 31.6%. At data cutoff, median (range) treatment exposure was 504.0 (56–1,054) days and mean ± standard deviation dose intensity was 154.4±77.5 mg/day. The most common treatment-emergent adverse events were nausea (n=14, 73.7%), decreased platelet count (n=12, 63.2%), decreased neutrophil count (n=11, 57.9%), anemia, vomiting, and decreased appetite (all n=9, 47.4%). One patient was diagnosed with treatment-related leukemia, which resulted in death. Median (95% confidence interval) progression-free survival was 18.0 (5.6–26.7) months. Conclusion: Overall, the safety profile of niraparib was considered manageable in this study population of Japanese patients with platinum-sensitive, relapsed ovarian cancer and was consistent with that observed in studies of non-Japanese patients. Trial Registration: ClinicalTrials.gov Identifier: NCT03759587
Daisuke Aoki,Aikou Okamoto,Tsutomu Tabata,Satoshi Yanagida,Toshiaki Nakamura,Eiji Kondo,Junzo Hamanishi,Kenichi Harano,Kosei Hasegawa,Takeshi Hirasawa,Kensuke Hori 대한부인종양학회 2024 Journal of Gynecologic Oncology Vol.35 No.5
Objective: To evaluate the long-term efficacy and safety of niraparib in Japanese women with heavily pretreated ovarian cancer. Methods: This was the follow-up analysis of a phase 2, multicenter, open-label, single-arm study in Japanese women with homologous recombination-deficient, platinum-sensitive, relapsed, high-grade serous epithelial ovarian, fallopian tube, or primary peritoneal cancer who had completed 3–4 lines of chemotherapy and were poly(ADP-ribose) polymerase inhibitor naïve. Participants received niraparib (starting dose, 300 mg) once daily in continuous 28-day cycles until objective disease progression, unacceptable toxicity, or consent withdrawal. The primary endpoint was confirmed objective response rate (ORR), as assessed using Response Evaluation Criteria in Solid Tumors version 1.1. Safety evaluations included treatment-emergent adverse events (TEAEs). Results: 20 patients were enrolled in the study and included in both efficacy and safety analyses. Median total study duration was 759.5 days. Median dose intensity was 201.3 mg/day. Confirmed ORR was 60.0% (90% confidence interval [CI]=39.4–78.3); 2 patients had complete response and 10 patients had partial response. Median duration of response was 9.9 months (95% CI=3.9–26.9) and the disease control rate was 90.0% (95% CI=68.3–98.8). The most common TEAEs were anemia (n=15), nausea (n=12), and decreased platelet count (n=11). TEAEs leading to study drug dose reduction, interruption, or discontinuation were reported in 16 (80.0%), 15 (75.0%), and 2 patients (10.0%), respectively. Conclusion: The long-term efficacy and safety profile of niraparib was consistent with previous findings in the equivalent population in non-Japanese patients. No new safety signals were identified. Trial Registration: ClinicalTrials.gov Identifier: NCT03759600