Approximation of functions by bivariate q-Stancu-Durrmeyer type operators

This paper is in continuation of our work in [24], wherein we studied someapproximation properties of the Stancu-Durrmeyer operators based on q-integers. Here,we construct a bivariate generalization of these operators and study the rate of convergenceby means of the complete modulus of continuity and the partial moduli of continuity andthe degree of approximation with the aid of the Peetre\u27s K functional. Subsequently, wedene the GBS(Generalized Boolean Sum) operators of Stancu- Durrmeyer type and givethe rate of approximation by means of the mixed modulus of smoothness and the Lipschitzclass of Bogel-continuous functions

ROLE OF PHALASARPI UTTARBASTI IN THE MANAGEMENT OF LOW ANTRAL FOLLICLES: A CASE STUDY

A female patient of 26 years old came into the OPD of Prasuti-Tantra at Choudhary Brahm Prakash Ayurveda Charaka Sansathan, Khera Dabar, New Delhi on dated 25/02/2017 with the complaint of wants to conceive since 3 years and scanty flow during menstrual cycle since 1year. On enquiry, she told that, she had miscarriage last year in January 2016 of gestational age 1month 6 days. Her menstrual cycle was irregular with duration of 3-5 days and interval of 28 to 32 days with scanty amount (1 pad/day) of menstrual blood and no other associated symptoms. She gave previous history of allopathic treatment. Her all Investigations regarding infertility had normal study except ultrasonography (USG) report which revealed Low antral follicles count. Aim of the management was to increase the Low Antral Follicles count as it is one of the cause of infertility and which represents poor ovarian reserve. So, the drug Phalasarpi as mentioned by Aacharya Vagbhatta for the conception was selected for Uttra Basti and Oral use as in- vivo effect of Phalasarpi in albino rat has revealed increased Gonadotropin secretion and regulation of the activity of the enzymes involved in ovarian steroidogenesis and stimulates serum estradiol level and proved to be successful in Anovulatory Infertility.

Quantitative-Voronovskaya and Grüss-Voronovskaya type theorems for Szász-Durrmeyer type operators blended with multiple Appell polynomials

Abstract In this paper, we establish a link between the Szász-Durrmeyer type operators and multiple Appell polynomials. We study a quantitative-Voronovskaya type theorem in terms of weighted modulus of smoothness using sixth order central moment and Grüss-Voronovskaya type theorem. We also establish a local approximation theorem by means of the Steklov means in terms of the first and the second order modulus of continuity and Voronovskaya type asymtotic theorem. Further, we discuss the degree of approximation by means of the weighted spaces. Lastly, we find the rate of approximation of functions having a derivative of bounded variation

Bezier variant of the Bernstein-Durrmeyer type operators

Acar, Tuncer/0000-0003-0982-9459WOS: 000414940700021In the present paper, we introduce the Bezier-variant of Durrmeyer modification of the Bernstein operators based on a function , which is infinite times continuously differentiable and strictly increasing function on [0, 1] such that and . We give the rate of approximation of these operators in terms of usual modulus of continuity and K-functional. Next, we establish the quantitative Voronovskaja type theorem. In the last section we obtain the rate of convergence for functions having derivative of bounded variation."Ministry of Human Resource Development" IndiaMinistry of Higher Education & Scientific Research (MHESR)The third author is thankful to the "Ministry of Human Resource Development" India for financial support to carry out the above research work

Stancu-Durrmeyer Type Operators Based on q-Integers

In this paper, we construct the Stancu-Durrmeyer-type modification of q-Bernstein operators by means of q-Jackson integral. Here, we establish moment estimates and some direct results which include basic convergence theorem, local approximation theorem and approximation for a Lipschitz type space. Also, we establish the Korovkin type A-statistical approximation theorem and rates of A-statistical convergence in terms of the modulus of continuity

Effect of apical negative irrigation on lateral canals of extracted teeth in endodontic treatment: An original research

Introduction: The aim of this study was to evaluate the efficacy of continuous apical negative ultrasonic irrigation into simulated lateral canals and the apical third in straight and curved root canals. Material and methods: Two simulated lateral canals were created 2, 4 and 6 mm from the working length in 120 single‑rooted teeth (6 canals/tooth, n = 360 straight, n = 360 curved). The teeth were randomly divided into 3 experimental groups: positive pressure irrigation (PPI) (n = 20); passive ultrasonic irrigation (PUI) (n = 20); continuous apical negative ultrasonic irrigation (CANUI) (n = 20). 20% Chinese ink was added to a 5% sodium hypochlorite solution and delivered into the root canals. Results: The results showed a significantly higher(P < 0.05) penetration of irrigant into the lateral canals and up to working length in the CANUI group for straight and curved roots. Conclusion: CANUI improves penetration into the lateral canals and up to the working length of the cleared teeth in straight and curved roots