• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1507-1518
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• 2010

In this article some generalized refinements of some inequalities for real quasi-cinvex, convex, concave, s-convex, s-concave, and $\alpha$-star s-convex mappings are obtained.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.567-574
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• 2018

Let $f:f(z)=z+{\sum^{{\infty}}_{n=2}}a_nz^n$ be analytic in the open unit disc E. Then f is said to belong to the class $M_{\alpha}$ of alpha-convex functions, if it satisfies the condition ${\Re}\{(1-{{\alpha})}{\frac{zf^{\prime}(z)}{f(z)}}+{{\alpha}}{\frac{(zf^{\prime}(z))^{\prime})}{f^{\prime}(z)}}\}$ > 0, ($z{\in}E$). In this paper, we introduce and study q-analogue of the class $M_{\alpha}$ by using concepts of Quantum Analysis. It is shown that the functions in this new class $M(q,{\alpha})$ are q-starlike. A problem related to q-Bernardi operator is also investigated.

• East Asian mathematical journal
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• v.21 no.2
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• pp.233-240
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• 2005

Let $CS^{\alpha}(\beta)$ denote the class of normalized strongly $\alpha$-logarithmic close-to-convex functions of order $\beta$, defined in the open unit disk $\mathbb{U}$ by $$\|arg\{\(\frac{f(z)}{g(z)}\)^{1-\alpha}\(\frac{zf'(z)}{g(z)\)^{\alpha}\}\|\leq\frac{\pi}{2}\beta,\;(\alpha,\beta\geq0)$$ where $g{\in}S^*$ the class of normalized starlike functions. In this paper, we prove sharp $Fekete-Szeg\"{o}$ inequalities for functions $f{\in}CS^{\alpha}(\beta)$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.165-173
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• 2018

In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^*({\alpha})$ of starlike functions of order ${\alpha}$ and $\mathcal{K}({\alpha}$) of convex functions of order ${\alpha}$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.107-115
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• 2004

In this paper, the new subclass denoted by $S_p({\alpha},{\beta},{\xi},{\gamma})$ of $p$-valent holomorphic functions has been introduced and investigate the several properties of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$. In particular we have obtained integral representation for mappings in the class $S_p({\alpha},{\beta},{\xi},{\gamma})$) and determined closed convex hulls and their extreme points of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.371-378
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• 2010

In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (${\alpha}$, m)-convex.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.35-43
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• 2013

In this paper, we introduce the notion of $t$-convex vague sets and study their properties in details.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.259-266
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• 2022

The present investigation is concerned with certain subclasses of alpha-convex functions with fixed point and defined with subordination in the unit disc E = {z :| z |< 1}. The estimates of the first four coefficients for the functions in these classes are obtained. The results due to various authors follow as special cases.

• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.307-317
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• 2012

In this paper we establish several Hadamard-type integral inequalities for (${\alpha}$, m)-convex functions.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.265-271
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• 2003

Let $CS_\alpha(\beta)$ denote the class of normalized strongly $\alpha$-close-to-convex functions of order $\beta$, defined in the open unit disk $\cal{U}$ of $\mathbb{C}$${\mid}arg{(1-{\alpha})\frac{f(z)}{g(z)}+{\alpha}\frac{zf'(z)}{g(z)}}{\mid}\;\leq\frac{\pi}{2}{\beta}(\alpha,\beta\geq0)$ such that $g\; \in\;S^{\ask}$, the class of normalized starlike unctions. In this paper, we obtain the sharp Fekete-Szego inequalities for functions belonging to $CS_\alpha(\beta)$.