• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.1077-1089
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• 2021

In this article, we introduce the quasi strongly E-convex function and pseudo strongly E-convex function on strongly E-convex set which generalizes strongly E-convex function defined by Youness [10]. Some non trivial examples have been constructed that show the existence of these functions. Several interesting properties of these functions have been discussed. An important characterization and relationship of these functions have been established. Furthermore, a nonlinear programming problem for quasi strongly E-convex function has been discussed.

• 충청수학회지
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• 제23권3호
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• pp.481-486
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• 2010

In this paper, we introduce the concepts of strongly c-convex( strongly c-concave) function, almost c-convex function on preconvex spaces. We investigate the relationships between such concepts and several types of preconvex sets.

• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.131-137
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• 2006

The object of the present paper is to obtain new conditions for analytic function to be strongly starlike and strongly convex function defined in the open unit disk.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.73-82
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• 2024

The purpose of this paper is to introduce a new subclass of strongly meromorphic close-to-convex functions by subordinating to generalized Janowski function. We investigate several properties for this class such as coefficient estimates, inclusion relationship, distortion property, argument property and radius of meromorphic convexity. Various earlier known results follow as particular cases.

• 대한수학회보
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• 제38권2호
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• pp.357-367
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• 2001

Let $Q(\beta)$ be the class of normalized strongly quasiconvex functions of order $\beta$ in the open unit disk. Sharp Fekete-Szego inequalities are obtained for functions belonging to the class $Q(\beta)$. We also consider the integral preserving properties in a sector.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.687-704
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• 2021

The refinement of an inequality provides better convergence of one quantity towards the other one. We have established the refinements of Hadamard inequalities for Riemann-Liouville fractional integrals via strongly (α, m)-convex functions. In particular, we obtain two refinements of the classical Hadamard inequality. By using some known integral identities we also give refinements of error bounds of some fractional Hadamard inequalities.

• 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 $f{\in}CS^{\alpha}(\beta)$.

• 대한수학회보
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• 제40권3호
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• pp.399-410
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• 2003

The purpose of the present paper is to introduce some new subclasses of strongly close-to-convex functions in the open unit disk defined by multiplier transformations and study their properties. Our results include several previous known results as special cases.

• 호남수학학술지
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• 제21권1호
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• pp.139-147
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• 1999

In this paper we generalize the definition of strongly close-to-convex functions by using the functions g(z) of bounded boundary rotation and investigate the distortion and rotation theorem, coefficient inequalities, invariance property and inclusion relation for the new class $G_{k}[A,\;B]$.

• 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.