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Partial Sums of Starlike Harmonic Univalent Functions
Porwal, Saurabh,Dixit, Kaushal Kishore Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.3
Although, interesting properties on the partial sums of analytic univalent functions have been investigated extensively by several researchers, yet analogous results on partial sums of harmonic univalent functions have not been so far explored. The main purpose of the present paper is to establish some new and interesting results on the ratio of starlike harmonic univalent function to its sequences of partial sums.
Convolution on a Generalized Class of Harmonic Univalent Functions
Porwal, Saurabh,Dixit, Kaushal Kishore Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.1
In the present paper, we introduce new subclasses of harmonic univalent functions and establish certain results concerning the convolution of functions for these subclasses. Relevant connections of the results presented here with various known results are briefly indicated.
On a Certain Integral Operator
Porwal, Saurabh,Aouf, Muhammed Kamal Department of Mathematics 2012 Kyungpook mathematical journal Vol.52 No.1
The purpose of the present paper is to investigate mapping properties of an integral operator in which we show that the function g defined by $$g(z)=\{\frac{c+{\alpha}}{z^c}{\int}_{o}^{z}t^{c-1}(D^nf)^{\alpha}(t)dt\}^{1/{\alpha}}$$. belongs to the class $S(A,B)$ if $f{\in}S(n,A,B)$.
Porwal, Saurabh Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.3
The purpose of the present paper is to investigate Confluent hypergeometric distribution. We obtain some basic properties of this distribution. It is worthy to note that the Poisson distribution is a particular case of this distribution. Finally, we give a nice application of this distribution on certain classes of univalent functions of the conic regions.
New Subclasses of Harmonic Starlike and Convex Functions
Porwal, Saurabh,Dixit, Kaushal Kishore Department of Mathematics 2013 Kyungpook mathematical journal Vol.53 No.3
The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes $V_H({\beta})$ and $U_H({\beta})$. Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.
RADII PROBLEMS OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS WITH FIXED SECOND COEFFICIENTS
PORWAL, SAURABH,BULUT, SERAP The Honam Mathematical Society 2015 호남수학학술지 Vol.37 No.3
The purpose of the present paper is to study certain radii problems for the function $$f(z)=\[{\frac{z^{1-{\gamma}}}{{\gamma}+{\beta}}}\(z^{\gamma}[D^nF(z)]^{\beta}\)^{\prime}\]^{1/{\beta}}$$, where ${\beta}$ is a positive real number, ${\gamma}$ is a complex number such that ${\gamma}+{\beta}{\neq}0$ and the function F(z) varies various subclasses of analytic functions with fixed second coefficients. Relevant connections of the results presented herewith various well-known results are briefly indicated.
RADII PROBLEMS OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS WITH FIXED SECOND COEFFICIENTS
( Saurabh Porwal ),( Serap Bulut ) 호남수학회 2015 호남수학학술지 Vol.37 No.3
The purpose of the present paper is to study certain radii problems for the function f(z)=[ {z ^{1-r}} over {r+ beta } ](z ^{r} [D ^{n} F(z)] ^{beta } )` ^{ 1/β} where - is a positive real number, ° is a complex number such that°+- 6= 0 and the function F(z) varies various subclasses of analytic functions with -xed second coe±cients. Relevant connections of the results presented herewith various well-known results are brie°y indicated.
Murugusundaramoorthy, Gangadharan,Porwal, Saurabh Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.4
The tenacity of the current paper is to find connections between various subclasses of analytic univalent functions by applying certain convolution operator involving generalized hypergeometric distribution series. To be more specific, we examine such connections with the classes of analytic univalent functions k - 𝓤𝓒𝓥<sup>*</sup> (𝛽), k - 𝓢<sup>*</sup><sub>p</sub> (𝛽), 𝓡 (𝛽), 𝓡<sup>𝜏</sup> (A, B), k - 𝓟𝓤𝓒𝓥<sup>*</sup> (𝛽) and k - 𝓟𝓢<sup>*</sup><sub>p</sub> (𝛽) in the open unit disc 𝕌.
Magesh, Nanjundan,Porwal, Saurabh,Themangani, Rajavadivelu Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.3
The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.
ON CERTAIN SUBCLASSES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH WRIGHT FUNCTION
NIRANJAN BASAVANTHAPPA GATTI,Saurabh Porwal,NANJUNDAN MAGESH 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.3
In the present investigation to obtain certain sufficient conditions for normalized Wright function to be in certain classes of starlike and convex functions defined in unit disc △ :={z∈C : |z|<}. Further, we obtain some inclusion relations and integral operator associated with Wright function.