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PRODUCT AND CONVOLUTION OF CERTAIN UNIVALENT FUNCTIONS
( Naveen Kumar Jain ),( V. Ravichandran ) 호남수학회 2016 호남수학학술지 Vol.38 No.4
For f<sub>i</sub> belonging to various subclasses of univalent func- tions, we investigate the product given by h(z) =zII _{i=1} ^{n} (f _{i} (z)/z) ^{yi} . The largest radius ½ is determined such that h(½z)=½ is starlike of orderβ, 0 · β < 1 or to belong to other subclasses of univalent functions. We also determine the sharp radius of starlikeness of order β and other radius for the convolution f ¤ g of two starlike functions f; g.
PRODUCT AND CONVOLUTION OF CERTAIN UNIVALENT FUNCTIONS
Jain, Naveen Kumar,Ravichandran, V. The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.4
For $f_i$ belonging to various subclasses of univalent functions, we investigate the product given by $h(z)=z{\prod_{i=1}^{n}}(f_i(z)/z)^{{\gamma}_i}$.The largest radius ${\rho}$ is determined such that $h({\rho}z)/{\rho}$ is starlike of order ${\beta}$, $0{\leq}{\beta}$ < 1 or to belong to other subclasses of univalent functions. We also determine the sharp radius of starlikeness of order ${\beta}$and other radius for the convolution f*g of two starlike functions f, g.
Pradeep Kumar Siddappa,Neha Jain,Naveen K. Agarwal,Monika Jain,Gurwant Singh Lamba 대한소화기내시경학회 2020 Clinical Endoscopy Vol.53 No.5
Background/Aims: Diagnostic abdominal paracentesis has been described in literature to have variable sensitivity of 50%–75% forthe detection of peritoneal carcinomatosis (PC). We believe that random needle aspirates from the omentum, even in the absence ofobvious deposits by endoscopic ultrasound (EUS), could prove malignancy in patients with PC. Methods: Consecutive patients who underwent EUS for diagnosis and staging of cancer and found to have ascites were includedafter obtaining informed consent. EUS-guided fine needle aspiration (EUS-FNA) from random sites in the omentum was performedthrough the transgastric route using a linear echoendoscope. Results: Fifty-four patients underwent EUS during October 2015 to April 2017 for detection, staging, or FNA of a suspectedmalignant lesion. Ascites was seen in 17 patients and 15 patients who fulfilled the criteria were included. The procedure wassuccessful in all patients. Cytology was suggestive of malignancy in 12 (80%) but not suggestive of malignancy in 3 (20%) patients. Three patients who tested negative had hyperbilirubinemia with biliary obstruction. Their ascitic fluid analysis result was alsonegative. Conclusions: Random FNA of the omentum in patients with malignancy-related ascites is highly effective in the diagnosis of PC andcould be employed during EUS evaluation of malignancies.
Analytic functions with conic domains associated with certain generalized $q$-integral operator
OM P. AHUJA,Asena Cetinkaya,Naveen Kumar Jain 대한수학회 2023 대한수학회논문집 Vol.38 No.4
In this paper, we define a new subclass of $k$-uniformly starlike functions of order $\gamma~ (0\leq\gamma<1)$ by using certain generalized $q$-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate $q$-sufficient coefficient condition, $q$-Fekete-Szeg\"{o} inequalities, $q$-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of $k$-uniformly convex functions of order $\gamma$ by using the generalized $q$-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.