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Solving Smooth Generalized Equations Using Modified Gauss-Type Proximal Point Method

Applied Mathematics 2022年第6期13卷 523-537页

作者： md. asraful alom md. Bayezid Gazi Imran Hossain Eshita Kundu Department of Mathematics Khulna University of Engineering & Technology Khulna Bangladesh

Consider X and Y are two real or complex Banach spaces. We introduce and study a modified Gauss-type proximal point algorithm (in short modified G-PPA) for solving the generalized equations of the form 0 ∈h(x) + H(x), where h : X → Y is a smooth function on Ω ⊆X and H : X ⇉2Y is a set valued mapping with closed graph. When H is metrically regular and under some sufficient conditions, we analyze both semi-local and local convergence of the modified G-PPA. Moreover, the convergence results of the modified G-PPA are justified by presenting a numerical example.

关键词： Set-Valued Mapping Metrically Regular Mapping Smooth Function Lipschitz-Like Mapping Semi-Local Convergence

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Convergence Analysis of General Version of Gauss-Type Proximal Point Method for Metrically Regular Mappings

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Applied Mathematics 2016年第11期7卷 1248-1259页

作者： md. asraful alom Mohammed Harunor Rashid Kalyan Kumer Dey Department of Mathematics University of Rajshahi Rajshahi Bangladesh Department of Mathematics Faculty of Civil Engineering Khulna University of Engineering & Technology Khulna Bangladesh

We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone acting from a Banach space X to a subset of a Banach space Y with locally closed graph. The convergence of the GG-PPA is present here by choosing a sequence of functions with , which is Lipschitz continuous in a neighbourhood O of the origin and when T is metrically regular. More precisely, semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a numerical example to validate the convergence result of GG-PPA.

关键词： Set-Valued Mappings Metrically Regular Mappings Lipschitz-Like Mapping Local and Semi-Local Convergence

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Journal of Diabetes Mellitus 2022年第4期12卷 243-251页

作者： md. Motiur Rahman Hafiza Sultana Farkhanda Mah Jebin Tanmoy Saha Wahida Yasmeen Foisal Mohammad Mosiul alom Syeda Tahmina Ferdous Jinia Syed Ahmed Laiak Ahammed Sheikh Sayera Khatun Medical College and Hospital Gopalganj Bangladesh National Institute of Preventive & Social Medicine (NIPSOM) Dhaka Bangladesh Khwaja Yunus Ali Medical College Sirajganj Bangladesh Tooth Fairy Foundation Dhaka Bangladesh Udayan Dental College Rajshahi Bangladesh National Institute of Traumatology and Orthopaedic Rehabilitation (NITOR) Dhaka Bangladesh Institute of Epidemiology Disease Control and Research (IEDCR) Dhaka Bangladesh Bangabandhu Sheikh Mujib Medical College Fraidpur Bangladesh

Introduction: The health related quality of life (HRQoL) has an important role in adults suffering from diabetes. Objective: To assess the health related quality of life in adult with type 2 diabetes mellitus. Materials and methods: A cross-sectional study was conducted to assess diabetic patient’s HRQoL on 119 purposively selected type-2 DM patients (aged ≥ 18 years and duration of diabetes ≥ 1 year). Data were collected by face-to-face interview and by medical record review through a Bangle version of SF-36 semi-structured questionnaire and a checklist. Place and period of study: The study was conducted at outpatient department in Gopalganj 50 bedded diabetic hospital from 1st January, 2018 to 31st December 2018. Results: The mean age of the respondents was 52.34 (SD ± 10.19) years. Age group shows a significant difference associated with all domains of quality of life except role emotion (>0.05), gender shows the significant in social and pain domain (0.05) respectively co-morbidity shows the significant difference with all domains expect pain (>0.05). Physical functioning, emotional, pain and general health of the quality of life show the significant difference associated with use of insulin (Conclusion: The overall QoL of type-2 DM patients was poor and had lower score of health related quality of life.

关键词： Type 2 Diabetes Mellitus Health Related Quality of Life Diabetes Mellitus

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