• Korean Journal of Mathematics
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• v.24 no.3
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.659-666
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• 2014

Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.85-91
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• 2011

We introduce and investigate the notions of super (g,g')-continuous functions and strongly $\theta$(g,g')-continuous functions on generalized topological spaces, which are strong forms of (g,g')-continuous functions. We also investigate relationships among such the functions, (g,g')-continuity and (${\delta},{\delta}'$)-continuity.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.119-130
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• 2006

A new class of functions is introduced in this paper. This class is called almost ${\delta}$-precontinuity. This type of functions is seen to be strictly weaker than almost precontinuity. By using ${\delta}$-preopen sets, many characterizations and properties of the said type of functions are investigated.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1025-1036
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• 2010

A new class of generalized open sets in a topological space, called e-open sets, is introduced and some properties are obtained by Ekici [6]. This class is contained in the class of $\delta$-semi-preopen (or $\delta-\beta$-open) sets and weaker than both $\delta$-semiopen sets and $\delta$-preopen sets. In order to investigate some different properties we introduce two strong form of e-open sets called e-regular sets and e-$\theta$-open sets. By means of e-$\theta$-open sets we also introduce a new class of functions called strongly $\theta$-e-continuous functions which is a generalization of $\theta$-precontinuous functions. Some characterizations concerning strongly $\theta$-e-continuous functions are obtained.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.4
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• pp.336-344
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• 2013

In this paper, we characterize the intuitionistic fuzzy ${\delta}$-continuous, intuitionistic fuzzy weakly ${\delta}$-continuous, intuitionistic fuzzy almost continuous, and intuitionistic fuzzy almost strongly ${\theta}$-continuous functions in terms of intuitionistic fuzzy ${\delta}$-closure and interior or ${\theta}$-closure and interior.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1531-1538
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• 2013

In the present investigation, the author introduces two interesting subclasses of normalized meromorphic univalent functions $w=f(z)$ defined on $\tilde{\Delta}:=\{z{\in}\mathbb{C}:1&lt;{\mid}z{\mid}&lt;{\infty}\}$ whose inverse $f^{-1}(w)$ is also univalent meromorphic in $\tilde{\Delta}$. Estimates for the initial coefficients are obtained for the functions in these new subclasses.

• Structural Engineering and Mechanics
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• v.70 no.6
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• pp.711-722
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• 2019

Considering stress singularities at point support locations, buckling solutions for plates with arbitrary number of point supports are hard to obtain. Thus, new Hp-Cloud shape functions with Kronecker delta property (HPCK) were developed in the present paper to examine elastic buckling of point-supported thin plates in various shapes. Having the Kronecker delta property, this specific Hp-Cloud shape functions were constructed through selecting particular quantities for influence radii of nodal points as well as proposing appropriate enrichment functions. Since the given quantities for influence radii of nodal points could bring about poor quality of interpolation for plates with sharp corners, the radii were increased and the method of Lagrange multiplier was used for the purpose of applying boundary conditions. To demonstrate the capability of the new Hp-Cloud shape functions in the domain of analyzing plates in different geometry shapes, various test cases were correspondingly investigated and the obtained findings were compared with those available in the related literature. Such results concerning these new Hp-Cloud shape functions revealed a significant consistency with those reported by other researchers.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.4
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• pp.24-32
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• 1985

This paper presents the design method for multivalued logic functions using $I^2L$ circuits. First, the a비orithm that transforms delta functions into discrete functions of a truncated difference is obtained. The realization of multivalued logic circuits by this algorithm is discussed. And then, the design method is achieved by mixing discrete functions and delta functions using the modified algorithm for given multivalued truth tables. The techniques discussed here are easily extended to multi-input and multi-output logic circuits.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1511-1524
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• 2019

In this paper, we investigate the uniqueness of meromorphic functions of finite order concerning sharing small functions and prove that if f(z) and ${\Delta}_cf(z)$ share a(z), b(z), ${\infty}$ CM, where a(z), b(z)(${\neq}{\infty}$) are two distinct small functions of f(z), then $f(z){\equiv}{\Delta}_cf(z)$. The result improves the results due to Li et al. ([9]), Cui et al. ([1]) and $L{\ddot{u}}$ et al. ([12]).