• Korean Journal of Mathematics
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• 제19권4호
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• pp.351-365
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• 2011

In the present paper we introduce a new subclass of analytic functions in the unit disc defined by convolution $(f_{\mu})^{(-1)}*f(z)$; where $$f_{\mu}=(1-{\mu})z_2F_1(a,b;c;z)+{\mu}z(z_2F_1(a,b;c;z))^{\prime}$$. Several interesting properties of the class and integral preserving properties of the subclasses are also considered.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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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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• 제21권2호
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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 $f{\in}CS^{\alpha}(\beta)$.

• Korean Journal of Mathematics
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• 제32권3호
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• pp.453-466
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• 2024

In the present paper, we define the class of (h₁, h₂, h₂)-preinvex functions on co-ordinates and prove certain new Hermite-Hadamard and Fejér type inequalities for such mappings. As a consequence, we derive analogous Hadamard-type results on convex and s-convex functions in three co-ordinates. We also discuss some intriguing aspects of the associated H function.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.467-478
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• 2013

The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes $V_H({\beta})$ and $U_H({\beta})$. Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.133-143
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• 2021

The purpose of this paper is to introduce and study certain subclasses of analytic functions by using Ruscheweyh derivative operator. We discuss various of interesting properties such as, necessary condition, arc length problem and growth rate of coefficient of newly defined class. Also rate of growth of Hankel determinant will be estimated.

• 호남수학학술지
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• 제41권1호
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• pp.89-99
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• 2019

The Steffensen's Inequality was discovered in 1918 by Johan Frederic Steffensen (1873-1961). This inequality is very popular in the research environment and attracted the attention of many people working in similar area. Various extensions and generalisations have been provided concerning the inequality. This paper presents some further refinements of the Steffensen's Inequality on Time scales using methods of convexity, differentiability and monotonicity.

• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.79-88
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• 1999

This work aims to establish an algorithm for solving the problem of convex programming with several objective-functions with linear constraints. Starting from the idea of Rosen's algorithm for solving the problem of convex programming with linear con-straints and taking into account the solution concept from multi-dimensional programming represented by a program which reaches "the best compromise" we are extending this method in the case of multidimensional programming. The concept of direction of min-imization is introduced and a necessary and sufficient condition is given for a s∈Rn direction to be a direction is min-imal. The two numerical examples presented at the end validate the algorithm.

• Korean Journal of Mathematics
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• 제31권1호
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• pp.75-94
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• 2023

We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly (s, m)-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.

• 대한수학회보
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• 제33권1호
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• pp.1-16
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• 1996

Earlier in 1935[12], M. S. Robertson introduced the class of quadrant preserving functions. More precisely, let Q be the class of all functions f(z) analytic in the unit disk $D = {z : $\mid$z$\mid$ < 1}$ such that f(0) = 0, f'(0) = 1, and the range f(z) is in the j-th quadrant whenever z is in the j-th quadrant of D, j = 1,2,3,4. This class Q contains the subclass of normalized, odd univalent functions which have real coefficients. On the other hand, this class Q is contained in the class T of odd typically real functions which was introduced by W. Rogosinski [13]. Clearly, if $f \in Q$, then f(z) is real when z is real and therefore the coefficients of f are all real. Recently, it was observed by Y. Abu-Muhanna and T. H. MacGregor [1] that any function $f \in Q$ is odd. Instead of functions "preserving quadrants", the authors [1] have introduced the notion of "preserving sectors".