Abstract. In this paper, we aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) (or (E.A)) property in the bicomplex valued metric spaces. We also provide some examples which support the main results here.

Background: Many patients with type 2 diabetes mellitus (T2DM) test positive for glutamic acid decarboxylase (GAD).These individuals have been referred to as having latent autoimmune diabetes in adults (LADA) or type 1.5 diabetes. LADA refers to a specific type of diabetes affecting adult patients, characterized by presence of islet auto-antibodies, insulin independence at the time of diagnosis and characterized by slower beta cell destruction. The aim of this study was to indentify GAD positivity in a selected group of Bangladeshi T2DM patients and compare the clinical characteristics of GAD positive and negative subjects. Methods: This cross-sectional study was conducted in 2017 at BIRDEM General Hospital, Dhaka. Recently diagnosed drug-naive patients with T2DM were evaluated. Considering inclusion and exclusion criteria 100 subjects were screened. These patients allowed for the assessment of GAD positivity along with anthropometric and biochemical characteristics. Results: A total of 100 newly diagnosed (within 6 months) T2DM patients in age group 30-70 years were selected for this study. Of them men and women were 59.6% and 40.4% respectively. The GAD antibody positive was found to be 10%. There was no significant difference in respect of age, body mass index, fasting plasma glucose, HbA1c, total cholesterol, triglycerides, HDL cholesterol, LDL and blood pressure between GAD positive and GAD negative subjects. Conclusion: The presence of GAD positivity was 10% among adult patients with newly diagnosed T2DM which wasvery high in Bangladeshi population. Further long term prospective studies need to be essential to identify the actual situation of GAD positive subjects and to determine their clinical course and optimal treatment regimens. Birdem Med J 2019; 9(3): 213-217

In this paper, we aim to establish and prove several results on common fixed point for pair of mappings satisfying more general contraction conditions portrayed by rational expressions in bicomplex valued metric spaces. Also, we introduced well-posedness and periodic point property of mappings satisfying a rational inequality in ordered bicomplex valued metric spaces.