• Kyungpook Mathematical Journal
• /
• v.47 no.3
• /
• pp.341-345
• /
• 2007

In this paper we show that the second order mock theta function, given by Hikami, is bounded and satisfies the second condition for the mock theta functions.

• East Asian mathematical journal
• /
• v.24 no.4
• /
• pp.329-338
• /
• 2008

The aim of this paper is to introduce a new generalization of fuzzy faintly continuous functions called fuzzy faintly pre-continuous functions and also we have introduced and studied weakly fuzzy pre-continuous functions. Several characterizations of fuzzy faintly pre-continuous functions are given and some interesting properties of the above functions are discussed.

• Kyungpook Mathematical Journal
• /
• v.56 no.1
• /
• pp.173-184
• /
• 2016

Mock theta functions are the most interesting topic mentioned in Ramanujan's Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.

• Journal of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.727-753
• /
• 2013

In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivex functions, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-pseudosounivex functions, and ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivexity assumptions for a multiobjective programming problem containing arbitrary norms.

• Korean Journal of Mathematics
• /
• v.20 no.4
• /
• pp.441-449
• /
• 2012

The quasi-(${\theta}$, s)-continuity is a weakened form of the weak (${\theta}$, s)-continuity and equivalent to the weak quasi-continuity. The basic properties of those functions are investigated in concern with the other weakened continuous functions. It turns out that the open property of a function and the extremall disconnectedness of the spaces are crucial tools for the survey of these functions.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2155-2163
• /
• 2017

Zwegers showed that a mock theta function can be completed to form essentially a real analytic modular form of weight 1/2 by adding a period integral of a certain weight 3/2 unary theta series. This theta series is related to the holomorphic modular form called the shadow of the mock theta function. In this paper, we discuss the computation of shadows of the second order mock theta functions and show that they share the same shadow with a mock theta function which appears in the Mathieu moonshine phenomenon.

• Kyungpook Mathematical Journal
• /
• v.45 no.2
• /
• pp.211-220
• /
• 2005

In this paper we obtain the transformations of the Ramanujan's tenth order mock theta functions under the modular group generators ${\tau}\;{\rightarrow}\;{\tau}\;+\;1\;and\;{\tau}\;{\rightarrow}\;-1/ {\tau}\;where\;q\;=\;e^{{\pi}it}$.

• Kyungpook Mathematical Journal
• /
• v.50 no.1
• /
• pp.165-175
• /
• 2010

In the paper we consider deemed three mock theta functions introduced by Hikami. We have given their alternative expressions in double summation analogous to Hecke type expansion. In proving we also give a new Bailey pair relative to $a^2$. I presume they will be helpful in getting fundamental transformations.

• East Asian mathematical journal
• /
• v.33 no.3
• /
• pp.291-293
• /
• 2017

We aim to present two identities which reveal certain interesting relationships among three fundamental theta functions arising from the Jacobi's triple product in an elementary way.

• Communications of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.371-381
• /
• 2013

In this paper, we investigate some properties of ${\theta}$-($\mathcal{G}$, $\mathcal{H}$)-continuous functions in a grill topological spaces. Moreover, the relationships with other related functions are investigated.