• Korean Journal of Mathematics
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• v.31 no.3
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• pp.269-294
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• 2023

The purpose of this paper is to introduce a new three-step iterative process and show that our iteration scheme is faster than other existing iteration schemes in the literature. We provide a numerical example supported by graphs and tables to validate our proofs. We also prove convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some weak and strong convergence theorems for nonexpansive mappings.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1876-1879
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• 1997

This paper developes an efficient algorithm for the minimum distance calculation between general polyhedra(convex and/or concave). The polyhedron approximates and object using flat polygons which composed of more than three veritices. The algorithm developed in this paper basically computes minimun distance betwen two convex polygons and finds a set of polygons whcih makes a global minimum distance. The advantage of the algorithm is that the global minimum distance can be computed in any cases. But the big disadvantage is that minimum distance computing time is repidly increased with the number of polygons which used to approximate an object. This paper developes a method to eliminate unnecessary sets of polygons, and an efficinet algorithm to compute a minimum distance between two polygons in order to compensate the inherent disadvantage of the algorithm. It takes only a few times iteration to find minimum distance for msot polygons. The correctness of the algortihm are visually tested with a line which connects two points making a global minimum distance of simple convex object(box) and concave object(pipe). The algorithm can find minimum distance between two convex objects made of about 200 polygons respectively less than a second computing time.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.583-595
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• 2016

Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle ${\Delta}ABP$. It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane ${\mathbb{R}}^2$, these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property $S={\frac{4}{3}}T$ for parabolas we study strictly locally convex curves in the plane ${\mathbb{R}}^2$ satisfying $S={\lambda}T+{\nu}U$, where ${\lambda}$ and ${\nu}$ are some functions on the curves. As a result, we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be an open arc of a parabola.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.661-670
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• 2005

In this paper, we deal with approximations of com­mon fixed points of the iterative sequences with errors for three asymptotically nonexpansive mappings in a uniformly convex Banach space. Our results generalize and improve the corresponding results of Khan and Takahashi, Schu, Takahashi and Tamura, and others.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.589-598
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• 2006

In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.313-321
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• 2017

In this note we establish a new non-convex hybrid iteration algorithm corresponding to Khan iterative process [4] and prove strong convergence theorems of common fixed points for a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in Hilbert spaces. Moreover, the main results are applied to get the common fixed points of finite family of quasi-asymptotically nonexpansive mappings. The results presented in this article are interesting extensions of some current results.

• East Asian mathematical journal
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• v.26 no.3
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• pp.429-440
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• 2010

In this paper, we study a new one-step iterative scheme with error for approximating common fixed points of non-self asymptotically nonexpansive in the intermediate sense mappings in uniformly convex Banach spaces. Also we have proved weak and strong convergence theorems for above said scheme. The results obtained in this paper extend and improve the recent ones, announced by Zhou et al. [27] and many others.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.169-182
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• 2011

The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc $\mathbb{U}$, which generalize the familiar class of k-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.75-98
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• 2021

In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szegö inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.155-160
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• 1986

Let X be a closed convex subset of a Banach space B and T:X.rarw.X a lipschitzian rotative map, i.e., such that ∥Tx-Ty∥.leq.k∥x-y∥ and ∥T$^{n}$ x-x∥.leq.a∥Tx-x∥ for some real k, a and an integer n>a. We denote by .PHI. (n, a, k, X) the family of all such maps. In [3], [4], K. Goebel and M. Koter obtained results concerning the existence of fixed points of T depending on k, a and n. In the present paper, the main results of [3], [4] are so strengthened that some information concerning the geometric estimations of fixed points are given.