In this paper, we introduce a relatively new class, $\mathcal{\mathcal{B}}_{1}^\BETA(\alpha)$, namely the class of BETA-Bazilevi\v{c} FUNCTION is generated by the FUNCTION Bazilevi\v{c} $\mathcal{B}_{1}(\alpha)$. We introduce the class in question by constructing the Alpha-Convex FUNCTION, $\mathcal{M}(\alpha)$, introduced by Miller et al. \cite{15}. Using Lemmas of FUNCTION with positive real part, we were given a sharp estimate of coefficient problems. The coefficient problems to be solved are the modulus of initial coefficients $f$, the modulus of inverse coefficients $f^{-1}$, the modulus of the Logarithmic coefficients $\log \frac{f(z)}{z}$, the Fekete-Szeg\"{o} problem and the second Hankel determinant problem.

Introduction. Renal involvement is a rare complication of β-thalassemia. Both tubular and glomerular dysFUNCTION might occur in these patients. The aim of this study was to evaluate and compare kidney FUNCTION in the major, intermedia, and minor variants of β-thalassemia. Materials and Methods. Renal tubular and glomerular FUNCTION of 72 patients with β-thalassemia (25 major, 23 intermedia, and 24 minor) were evaluated. Patients older than 40 years and those with chronic kidney disease, diabetes mellitus, congestive heart failure, associated infections, congenital anomalies of the kidney and urinary tract were excluded. Blood and urine samples were collected electrolytes and markers of kidney FUNCTION. Results. Mean age at the time of study was significantly higher in the minor group. The majority of patients with thalassemia major were males. Hematuria and pyuria occurred in 4% to 8% of the patients. Serum level of all variables were within normal limits, with no significant difference between the three groups. Glomerular filtration rate was nonsignificantly higher in the major and intermedia groups, compared to the minor variant. A significantly lower urine phosphorus and uric acid excretion was noted with the minor variant. Urine phosphorus and uric acid excretion increased more frequently in the major and intermedia groups. Conclusions. Tubular and glomerular FUNCTIONs appear to be well preserved in all variants of β-thalassemia.

In the present research, we will deal with mean square integral inequalities for preinvex stochastic process and η-convex stochastic process in the setting of BETA FUNCTION. Further, we will present some novel results for improved H¨older integral inequality. The results given in this present paper are generalizations of already existing results in the literature.

Kernel estimation of the cumulative distribution FUNCTION (CDF), when the support of the data is bounded, suffers from bias at the boundaries. To solve this problem, we introduce a new estimator for the CDF with support (0,1) based on the BETA kernel FUNCTION. By studying the asymptotic properties of the proposed estimator, we show that it is consistent and free from boundary bias. We conducted an extensive simulation to illustrate the performance of the proposed estimator. The results demonstrate the superiority of the proposed estimator over other commonly used estimators. As an application, we use the estimated CDF for nonparametric simulation. Using a numerical study, we show that the performance of the kernel probability density FUNCTION (PDF) estimation in which a large sample simulated from the estimated CDF is employed can be noticeably improved. We also use the proposed estimator to estimate the CDF of the household health cost in Iran in 2019.

Introduction: Compared to the conventional methods, serum BETA-trace protein (BTP) has been shown to be more helpful for estimating glomerular filtration rate; however, its value is remained unclear in neonates. The present study aimed to investigate the range of serum BTP level in healthy term neonates and its value to estimate glomerular filtration rate.Materials and Methods: This cross-sectional study was conducted on 50 healthy term neonates without underlying cardiovascular or kidney disorders who were admitted to Ali Asghar hospital in 2013. Serum BTP was measured using an automated nephelometric immunoassay. Glomerular filtration rate was assessed using the Schwartz equation based on serum creatinine level.Results: The mean age of the neonates was 6.2±3.6 days (range, 2 to 17 days), their mean gestational age was 38.02±0.20 weeks, and their mean height was 49.8±1.7 cm. The mean serum BTP level was 0.41±0.11 mg/L (range, 0.19 mg/L to 0.92 mg/L). The mean serum creatinine level was 0.49±0.16 mg/dL (range, 0.3 mg/dL to 1.0 mg/dL). The mean estimated GFR was 48.90±15.88 mL/ min. A positive correlation was observed between the reciprocal concentrations of BTP and GFR (r=0.383, P=.006). Furthermore, the reciprocal concentrations of BTP was associated with the reciprocal concentrations of serum creatinine level (r=0.365, P=.009).Conclusions: Measurement of serum BTP can be a reliable tool for detecting kidney FUNCTION in neonates. Further studies are warranted to design a suitable formula for GFR estimation based on serum BTP in neonates.

In this paper, we are introducing for the first time a generalized class named the class of $(\alpha,\BETA,\gamma,\delta)-$convex FUNCTIONs of mixed kind. This generalized class contains many subclasses including the class of $(\alpha,\BETA)-$convex FUNCTIONs of the first and second kind, $(s,r)-$convex FUNCTIONs of mixed kind, $s-$convex FUNCTIONs of the first and second kind, $P-$convex FUNCTIONs, quasi-convex FUNCTIONs and the class of ordinary convex FUNCTIONs. In addition, we would like to state the generalization of the classical Ostrowski inequality via fractional integrals, which is obtained for FUNCTIONs whose first derivative in absolute values is $(\alpha,\BETA,\gamma,\delta)-$ convex FUNCTION of mixed kind. Moreover, we establish some Ostrowski-type inequalities via fractional integrals and their particular cases for the class of FUNCTIONs whose absolute values at certain powers of derivatives are $(\alpha,\BETA,\gamma,\delta)-$ convex FUNCTIONs of mixed kind using different techniques including H\"older's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, the applications of special means will also be discussed.