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ON CERTAIN GENERALIZED q-INTEGRAL OPERATORS OF ANALYTIC FUNCTIONS
Sunil Dutt Purohit,Kuppathai Appasamy Selvakumaran 대한수학회 2015 대한수학회보 Vol.52 No.6
In this article, we first consider a linear multiplier fractional q-differintegral operator and then use it to define new subclasses of p- valent analytic functions in the open unit disk U. An attempt has also been made to obtain two new q-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.
ON CERTAIN GENERALIZED q-INTEGRAL OPERATORS OF ANALYTIC FUNCTIONS
PUROHIT, SUNIL DUTT,SELVAKUMARAN, KUPPATHAI APPASAMY Korean Mathematical Society 2015 대한수학회보 Vol.52 No.6
In this article, we first consider a linear multiplier fractional q-differintegral operator and then use it to define new subclasses of p-valent analytic functions in the open unit disk U. An attempt has also been made to obtain two new q-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.
On a q-Extension of the Leibniz Rule via Weyl Type of q-Derivative Operator
Purohit, Sunil Dutt Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.4
In the present paper we define a q-extension of the Leibniz rule for q-derivatives via Weyl type q-derivative operator. Expansions and summation formulae for the generalized basic hypergeometric functions of one and more variables are deduced as the applications of the main result.
Choi, Junesang,Purohit, Sunil Dutt Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.2
In this paper, we aim at establishing a generalized fractional integral version of Gr$\ddot{u}$ss type integral inequality by making use of the Gauss hypergeometric function fractional integral operator. Our main result, being of a very general character, is illustrated to specialize to yield numerous interesting fractional integral inequalities including some known results.
INTEGRAL REPRESENTATIONS OF THE k-BESSEL`S FUNCTION
( Kuldeep Singh Gehlot ),( Sunil Dutt Purohit ) 호남수학회 2016 호남수학학술지 Vol.38 No.1
This paper deals with the study of newly defined special function known as k-Bessel`s function due to Gehlot [2]. Certain integral representations of k-Bessel`s function are investigated. Known integrals of classical Bessel`s function are seen to follow as special cases of our main results.
On Applications of Weyl Fractional q-integral Operator to Generalized Basic Hypergeometric Functions
Yadav, Rajendra Kumar,Purohit, Sunil Dutt Department of Mathematics 2006 Kyungpook mathematical journal Vol.46 No.2
Applications of Weyl fractional $q$-integral operator to various generalized basic hypergeometric functions including the basic analogue of Fox's H-function have been investigated in the present paper. Certain interesting special cases have also been deduced.
Integral Formulas Involving a Product of Generalized Bessel Functions of the First Kind
Choi, Junesang,Kumar, Dinesh,Purohit, Sunil Dutt Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.1
The main object of this paper is to present two general integral formulas whose integrands are the integrand given in the integral formula (3) and a finite product of the generalized Bessel function of the first kind.
INTEGRAL REPRESENTATIONS OF THE k-BESSEL'S FUNCTION
Gehlot, Kuldeep Singh,Purohit, Sunil Dutt The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.1
This paper deals with the study of newly defined special function known as k-Bessel's function due to Gehlot [2]. Certain integral representations of k-Bessel's function are investigated. Known integrals of classical Bessel's function are seen to follow as special cases of our main results.
THE COMPOSITION OF HURWITZ-LERCH ZETA FUNCTION WITH PATHWAY INTEGRAL OPERATOR
Jangid, Nirmal Kumar,Joshi, Sunil,Purohit, Sunil Dutt,Suthar, Daya Lal Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.2
The aim of the present investigation is to establish the composition formulas for the pathway fractional integral operator connected with Hurwitz-Lerch zeta function and extended Wright-Bessel function. Some interesting special cases have also been discussed.
ON BASIC ANALOGUE OF CLASSICAL SUMMATION THEOREMS DUE TO ANDREWS
( Harsh Vardhan Harsh ),( Arjun K. Rathie ),( Sunil Dutt Purohit ) 호남수학회 2016 호남수학학술지 Vol.38 No.1
In 1972, Andrews derived the basic analogue of Gauss`s second summation theorem and Bailey`s theorem by implementing basic analogue of Kummer`s theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer`s theorem, Gauss`s second summation theorem and Bailey`s theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer`s theorem. The aim of this paper is to derive basic analogues of results closely related Gauss`s second summation theorem and Bailey`s theorem. Some applications and limiting cases are also considered.