By using generalized Montgomery identity and Green functions we proved several identities which assist in developing connections with Steffensen's inequality. Under the assumptions of n-convexity and n-concavity many inequalities, which generalize Steffensen's inequality, inequalities from (Fahad et al. in their reverse, have been proved. Generalization of some inequalities (and their reverse) which are related to Hardy-type inequality (Fahad et al. in J. Math. Inequal. 9:481-487, 2015) have also been proved. New bounds of Ostrowski and Grüss type inequalities have been developed. Moreover, we formulate generalized Steffensen-type linear functionals and prove their monotonicity for the generalized class of (n + 1)-convex functions at a point. At the end, we present some applications of our study to the theory of exponentially convex functions. MSC: Primary 26D10; secondary 26D20Keywords: Steffensen's inequality; Green's function; Montgomery's identity; (n + 1)-convex function at a point c+θ c ψ(z) dz, where θ = d c f (z) dz.( 1 )A massive literature body dealing with several variants and improvements of (1) can be seen in [14,16] and the references therein. Pečarić [13] gave a nice generalization of (1) as follows.
Introduction: Pyloric stenosis is an uncommon condition in infants characterized by abnormal thickening of the pylorus muscles in the stomach leading to gastric outlet obstruction. Clinically infants are well at birth. Then, at 3 to 6 weeks of age, the infants present with "projectile" vomiting which can lead to dehydration and weight loss. Objective: To determine the frequency of pyloric stenosis in patient presenting with persistent vomiting. Material and Method: This Cross Sectional Study was conducted in the department of Gastroenterology, ATH, Abbottabad from 5th October 2020 to 5th April 2021. A total of 115 patients of both gender with persistent vomiting for more than 5 days were included in the study. Abdominal ultrasound was done by a consultant gastroenterologist of three years post fellowship experience. Pyloric stenosis was noted. Results: Age range in this study was from 1 to 40 years with mean age of 6.226±6.62 years and mean duration of complaints was 9.869±3.76 days. Male patients were 88.7%% and females were 11.3%%. Pyloric Stenosis was observed in 93% patients. Conclusion: Our study concluded that that pyloric stenosis is 4 times more common in males compared to females and is more common among younger age groups as compared to adult patients. Keywords: Persistent vomiting, pyloric stenosis, Ultrasound, Frequency
Background; Obstructive jaundice in simple terms means the outflow of bile has been obstructed anywhere from the liver to the duodenum. It is caused by obstruction, blockage and/or compression of common bile duct (CBD) and/or biliary tract that leads to incomplete excretion of bile into the intestine. Patients with obstructive jaundice usually present with Complains of abdominal pain, yellow discoloration of skin and/or eyes, pale stools, dark colored urine, nausea, vomiting and pruritus. Objective: To determine frequency of common bile duct strictures in patients presenting with obstructive jaundice in Ayub teaching hospital. Material and Method. This Cross Sectional Study was conducted in the department of Gastroenterology, ATH, Abbottabad from 15th September 2020 to 15th March 2021. A total of 135 patients of both gender presenting with jaundice and having serum bilirubin ≥1.1 mg/dl, alkaline phosphatase ≥140 IU/L along with evidence of obstruction of common bile duct were included in the study. Presence of CBD stricture was confirmed through Ultrasonography or CT abdomen. Results: Age range in this study was from 20 to 80 years with mean age of 44.651±12.90 years. Female gender was dominant with 61.5% patients. Common bile duct strictures was seen in 9.6% patients.
Introduction: Anemia appears to be the most common extra intestinal manifestation of inflammatory bowel disease and has been associated with a wide range of complications such as impaired quality of life, an increased rate of hospital admissions and even mortality. Objective: To determine the frequency of anemia in patients presenting with ulcerative colitis. Material and methods;This Cross Sectional Study was conducted in the Department of Gastroenterology, ATH, Abbottabad from 20th September 2020 to 20th March 2021. A total of 109 patients of both gender with ulcerative colitis were included in the study. Venous blood was collected from all patients in sodium EDTA tube by a 3rd year resident and was immediately sent to hospital laboratory. Hemoglobin < 11 g/dL was recorded as anemia and noted. Results: Age range in this study was from 18 to 60 years with mean age of 41.550±6.56 years, mean duration of complain was 9.862±2.57 months and mean weight was 80.091±7.60 Kg. Male patients were 63.3% and females were 36.7%. Anemia was observed in 14.7% Patients presenting with ulcerative colitis. Conclusion: In conclusion, we found a high incidence and prevalence of anaemia in patients presenting with ulcerative colitis.
Channels filled with coarse‐grained sands are one of the hot issues in stratigraphic explorations. However, the sub‐surface uncertainty restricts the prediction of porous channel sandstones using the conventional seismic attributes, which is a concern for the demarcation of stratigraphic plays. The amplitude‐based frequency attributes and seismic‐petrophysical simulation tools were applied to characterize the fluvial channel system from the Indus Basin, Pakistan. The conventional amplitude of the Basal Sand Formation shows limited imaging ability to detect the dimensions of channel‐levee and point bars. The continuous wavelet transforms (CWT) tool distinguishes the whole channel‐levee reservoir system at tuning frequencies of 21, 25, 29, and 34 Hz. The amplitudes extracted along the pseudo‐porosity wells depict the low‐density and low‐velocity profiles within the gas‐bearing zones. The zone between 20% and 30% porosity displays low‐density and low‐velocity compartments within the point bars. Hence, it implicates the zone of deposition for hydrocarbon‐bearing fluvial facies. Based on the porosity constraint, the gas‐bearing fluvial reservoirs have high (>25%) porosity, which implicates the development of aggradational parasequences. The oil‐dominated sandstone facies experience relatively low‐porosity of <12% and negligibly high density and high velocity, which implicates the development of transgressive parasequences. The reservoir system shows an eastward shale‐out zone, where the high‐density and high‐velocity shales mask the channel‐levee systems. Consequently, these stratigraphic configurations are developing into a cost‐effective stratigraphic trap, and hence, this exploration scheme serves as an analogue for global fluvial depositional systems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.