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We consider functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications are found to the theory of semigroups. [ABSTRACT FROM AUTHOR]

Background: Diabetes mellitus is a highly prevalent and growing chronic disease affecting an estimated 415 million people globally in 2015, and is predicted to affect 642 million people by 2040. India has more than 69 million people with T2DM, and these numbers are expected to rise to 140 million by 2040. Diet constitutes a crucial aspect of the overall management of diabetes, which may involve diet alone, diet with oral hypoglycemic drugs, or diet with insulin. Objectives: 1. To identify the various dietary habits in relation to type 2 diabetes mellitus among adults in urban population of Eluru. 2. To study the drug pattern in diabetic individuals of the study population. Materials and method: This was a community based cross-sectional study conducted in the urban area of Eluru for a period of one year among 454 adults 30 years and above age group. The data was collected using a pretested semi-structured questionnaire by interview method. Results were analyzed and necessary statistical tests were applied. Results: Out of 454 study population 96 were diabetic individuals showing the prevalence of diabetes as 21.1%. Prevalence of diabetes was high (28.1%) among study subjects who were consuming rice as their staple diet (p<0.05). There was a statistical significant association (p<0.05) found between germinating seeds consumption and diabetes mellitus. Conclusion: Diabetic individuals should be encouraged to adhere to the strict dietary advice. All the individuals were advised to add the germinating seeds to their daily consuming diet. Simple dietary modifications like avoidance of junk foods will prevent or delay the onset of type 2 diabetes mellitus. [ABSTRACT FROM AUTHOR]