• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.461-470
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• 2024

In this paper, a new subclass, 𝒮𝒞^𝜇,p,q_𝜎 (r, s; x), of Sakaguchitype analytic bi-univalent functions defined by (p, q)-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for |a₂| and |a₃| are obtained. Fekete-Szegö inequalities for the class are found. Finally, we give some corollaries.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.465-478
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• 2006

In this paper, we introduce a new class of completely generalized strongly nonlinear quasivariational inequalities and establish its equivalence with a class of fixed point problems by using the resolvent operator technique. Utilizing this equivalence, we develop a three-step iterative scheme with errors, obtain a few existence theorems of solutions for the completely generalized non-linear strongly quasivariational inequality involving relaxed monotone, relaxed Lipschitz, strongly monotone and generalized pseudocontractive mappings and prove some convergence and stability results of the sequence generated by the three-step iterative scheme with errors. Our results include several previously known results as special cases.

• Journal of the Korean Operations Research and Management Science Society
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• v.37 no.4
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• pp.67-72
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• 2012

In this paper a new method of handling linear constraints for the genetic algorithm is suggested. The method is designed to maintain the feasibility of offsprings during the evolution process of the genetic algorithm. In the genetic algorithm, the chromosomes are coded as the vectors in the real vector space constrained by the linear constraints. A method of handling the linear constraints already exists in which all the constraints of equalities are eliminated so that only the constraints of inequalities are considered in the process of the genetic algorithm. In this paper a new method is presented in which all the constraints of inequalities are eliminated so that only the constraints of equalities are considered. Several genetic operators such as arithmetic crossover, simplex crossover, simple crossover and random vector mutation are designed so that the resulting offspring vectors maintain the feasibility subject to the linear constraints in the framework of the new handling method.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.105-118
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• 2007

In this paper, we first define a new kind of two-weight-$A_r^{{\lambda}_3}({\lambda}_1,{\lambda}_2,{\Omega})$-weight, and then prove the imbedding inequalities for $\mathcal{A}$-harmonic tensors. These results can be used to study the weighted norms of the homotopy operator T from the Banach space $L^p(D,{\bigwedge}^l)$ to the Sobolev space $W^{1,p}(D,{\bigwedge}^{l-1})$, $l=1,2,{\cdots},n$, and to establish the basic weighted $L^p$-estimates for $\mathcal{A}$-harmonic tensors.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.543-552
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• 2006

The purpose of the present paper is to introduce two novel subclasses $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$ and $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$. These results are then appropriately applied to derive similar geometrical properties for the other class $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1315-1325
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• 2021

In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝⁿ. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the (k + 1)^th eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.307-332
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• 2024

Two inertial extragradient-type algorithms are introduced for solving convex pseudomonotone variational inequalities with fixed point problems, where the associated mapping for the fixed point is a 𝜌-demicontractive mapping. The algorithm employs variable step sizes that are updated at each iteration, based on certain previous iterates. One notable advantage of these algorithms is their ability to operate without prior knowledge of Lipschitz-type constants and without necessitating any line search procedures. The iterative sequence constructed demonstrates strong convergence to the common solution of the variational inequality and fixed point problem under standard assumptions. In-depth numerical applications are conducted to illustrate theoretical findings and to compare the proposed algorithms with existing approaches.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.319-330
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• 2020

We introduce a new subclass of q-bi-univalent functions of complex order related to shell-like curves connected with the Fibonacci numbers. We obtain the coefficient estimates and Fekete-Szegö inequalities for the functions belonging to this class. Relevant connections with various other known classes have been illustrated.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.261-267
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• 2006

A local convergence analysis of Newton's method for perturbed generalized equations is provided in a Banach space setting. Using center Lipschitzian conditions which are actually needed instead of Lipschitzian hypotheses on the $Fr\'{e}chet$-derivative of the operator involved and more precise estimates under less computational cost we provide a finer convergence analysis of Newton's method than before [5]-[7].

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.881-891
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• 2012

In this paper we investigate the approximate controllability for the following nonlinear functional differential control problem: $$x^{\prime}(t)+Ax(t)+{\partial}{\phi}(x(t)){\ni}f(t,x(t))+h(t)$$ which is governed by the variational inequality problem with nonlinear terms.