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An Integrated Approach to Teaching and Learning College Mathematics
Ahuja, Om P,Jahangiri, Jay M 한국수학교육학회 2003 수학교육연구 Vol.7 No.1
The key features of our integrated approaching and learning college mathematics include interactive and discussion-based teaching, small group work, computer as a tool, problem solving approach, open approach, mathematics in context, emphasis on mathematical thinking and creativity, and writing/communicating about mathematics. In this paper we report a few examples to illustrate the type of problems we use in our integrated approach.
On a Linear Combination of Classes of Multivalently Harmonic Functions
OM P. AHUJA,JAY M. JAHANGIRI 경북대학교 자연과학대학 수학과 2002 Kyungpook mathematical journal Vol.42 No.1
New classes of multivalent harmonic functions are introduced. We give sufficient coefficient conditions for these classes. These coefficient conditions are shown to be also necessary if certain restrictions are imposed on the coefficients of these harmonic functions. Furthermore, we determine a representation theorem, inclusion relations, and distortion bounds for these functions.
Om Ahuja,Nisha Bohra,Asena Cetinkaya,Sushil Kumar 경북대학교 자연과학대학 수학과 2021 Kyungpook mathematical journal Vol.61 No.1
In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szeg¨o inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.
Spirallike and Robertson Functions of Complex Order with Bounded Boundary Rotations
Ahuja, Om,Cetinkaya, Asena,Kahramaner, Yasemin Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.2
Using the concept of bounded boundary rotation, we investigate various properties of two new generalized classes of spirallike and Robertson functions of complex order with bounded boundary rotations.
Multivalent Harmonic Uniformly Starlike Functions
Ahuja, Om,Joshi, Santosh,Sangle, Naveneet Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.3
In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.
SYMMETRIC TOEPLITZ DETERMINANTS ASSOCIATED WITH A LINEAR COMBINATION OF SOME GEOMETRIC EXPRESSIONS
( Om P. Ahuja ),( KANIKA KHATTER ),( V. Ravichandran ) 호남수학회 2021 호남수학학술지 Vol.43 No.3
Let f be the function defined on the open unit disk, with f(0) = 0 = f′(0) - 1, satisfying Re (αf′(z) + (1 - α)zf′(z)/f(z)) > 0 or Re (αf′(z) + (1 - α)(1 + zf′′(z)/f′(z)) > 0 respectively, where 0 ≤ α ≤ 1. Estimates for the Toeplitz determinants have been obtained when the elements are the coefficients of the functions belonging to these two subclasses.
Upper bounds of second Hankel determinant for universally prestarlike functions
Om Ahuja,Murugesan Kasthuri,GANGADHARAN. MURUGUSUNDARAMOORTHY,Kaliappan Vijaya 대한수학회 2018 대한수학회지 Vol.55 No.5
In \cite{Rusche1,Rusche2} the researchers introduced universally convex, universally starlike and universally prestarlike functions in the slit domain $\mathbb{C}\backslash \lbrack 1,\infty )$. These papers extended the corresponding notions from the unit disc to other discs and half-planes containing the origin. In this paper, we introduce universally prestarlike generalized functions of order $\alpha $ with $\alpha \leq 1$ and we obtain upper bounds of the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for such functions.
UPPER BOUNDS OF SECOND HANKEL DETERMINANT FOR UNIVERSALLY PRESTARLIKE FUNCTIONS
Ahuja, Om,Kasthuri, Murugesan,Murugusundaramoorthy, Gangadharan,Vijaya, Kaliappan Korean Mathematical Society 2018 대한수학회지 Vol.55 No.5
In [12,13] the researchers introduced universally convex, universally starlike and universally prestarlike functions in the slit domain ${\mathbb{C}}{\backslash}[1,{\infty})$. These papers extended the corresponding notions from the unit disc to other discs and half-planes containing the origin. In this paper, we introduce universally prestarlike generalized functions of order ${\alpha}$ with ${\alpha}{\leq}1$ and we obtain upper bounds of the second Hankel determinant ${\mid}a_2a_4-a^2_3{\mid}$ for such functions.
Ahuja, Om P.,Cetinkaya, Asena,Bohra, Nisha The Honam Mathematical Society 2020 호남수학학술지 Vol.42 No.2
We introduce a new subclass of q-bi-univalent functions of complex order related to shell-like curves connected with the Fibonacci numbers. We obtain the coefficient estimates and Fekete-Szegö inequalities for the functions belonging to this class. Relevant connections with various other known classes have been illustrated.
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.