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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.
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.
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.
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.
Geometric properties of starlikeness involving hyperbolic cosine function
OM P. AHUJA,Asena Cetinkaya,Sushil Kumar 대한수학회 2024 대한수학회논문집 Vol.39 No.2
In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.