• 충청수학회지
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• 제22권3호
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• pp.319-324
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• 2009

In a series of papers [3, 4, 5], the author developed the generalized vector variational inequality with operator solutions (in short, GOVVI) by exploiting variational inequalities with operator solutions (in short, OVVI) due to Domokos and $Kolumb\acute{a}n$ [2]. In this note, we give an extension of the previous work [4] in the setting of Hausdorff locally convex spaces. To be more specific, we present an existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [7] within the framework of (GOVVI).

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1235-1246
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• 2009

In this paper, we prove existence results for first order impulsive evolution differential inclusions with nonlocal condition by using a fixed point theorem for condensing multi-valued maps. An example is also given to illustrate the obtained results.

• 대한수학회지
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• 제48권3호
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• pp.585-597
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• 2011

We prove the existence and uniqueness of classical solutions for a quasilinear delay integrodifferential equation in Banach spaces. The result is established by using the semigroup theory and the Banach fixed point theorem.

• 대한수학회지
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• 제57권3호
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• pp.617-640
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• 2020

In this paper, we introduce a parallel iterative method for finding a common fixed point of a finite family of Bregman strongly nonexpansive mappings in a real reflexive Banach space. Moreover, we give some applications of the main theorem for solving some related problems. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.

• 대한수학회보
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• 제28권2호
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• pp.163-174
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• 1991

This is a continuation of the author's previous work [17]. In this paper, we consider mainly variational inequalities for single-valued functions. We first obtain a generalization of the variational type inequality of Juberg and Karamardian [10] and apply it to obtain strengthened versions of the Hartman-Stampacchia inequality and the Brouwer fixed point theorem. Next, we obtain fairly general versions of Browder's variational inequality [5] and its subsequent generalizations due to Brezis et al [4], Takahashk [23], Shih and Tan [19], Simons [20], and others. Finally, in this paper, we obtain a variational inequality for non-real locally convex t.v.s. which generalizes a result of Shih and Tan [19].

• 대한수학회논문집
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• 제24권1호
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• pp.29-40
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• 2009

Motivated by [Linear Algebra and its Appl. 420(2007), 218-227] and [Linear Algebra and its Appl. 425(2007), 171-183], we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional difference equations with p-Laplacian. Sufficient conditions for the existence of at least one solution of this problem are established.

• 대한수학회지
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• 제50권3호
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• pp.627-639
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• 2013

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H$\ddot{o}$lder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.

• Kyungpook Mathematical Journal
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• 제48권4호
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• pp.637-650
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• 2008

New sufficient conditions for the existence of at least one solution of Neumann type boundary value problems for second order nonlinear differential equations $$\array{\{{p(t)\phi(x'(t)))'=f(t,x(t),\;x(\tau_1(t)),\;{\cdots},\;x(\tau_m(t))),\;t\in[0,T],\\x'(0)=0,\;x'(T)=0,}\,}$$, are established.

• East Asian mathematical journal
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• 제26권1호
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• pp.81-93
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• 2010

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.

• East Asian mathematical journal
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• 제27권5호
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• pp.585-595
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• 2011

In this paper, we introduce and study a new class of strongly nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of strongly nonlinear variational- like inequalities. By making use of the auxiliary principle technique, we suggest an iterative algorithm for the strongly nonlinear variational-like inequality and give the convergence criteria of the sequences generated by the iterative algorithm.