• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.939-958
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• 2021

Some properties of strongly Gorenstein C-projective, C-injective and C-flat modules are studied, mainly considering these properties under change of rings. Specifically, the completions of rings, the localizations and the polynomial rings are considered.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.203-219
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• 2018

This paper is devoted to the study of strongly ${\alpha}-semicommutative$ rings, a generalization of strongly semicommutative and ${\alpha}-rigid$ rings. Although the n-by-n upper triangular matrix ring over any ring with identity is not strongly ${\bar{\alpha}}-semicommutative$ for $n{\geq}2$, we show that a special subring of the upper triangular matrix ring over a reduced ring is strongly ${\bar{\alpha}}-semicommutative$ under some additional conditions. Moreover, it is shown that if R is strongly ${\alpha}-semicommutative$ with ${\alpha}(1)=1$ and S is a domain, then the Dorroh extension D of R by S is strongly ${\bar{\alpha}}-semicommutative$.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.861-870
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• 2007

In this paper, under suitable conditions, we show that the new class of iterative process with errors introduced by Li et al converges strongly to the unique solution of the equation involving strongly accretive operators in real Banach spaces. Furthermore, we prove that it is equivalent to the classical Ishikawa iterative sequence with errors.

• 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 applied mathematics & informatics
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• v.5 no.1
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• East Asian mathematical journal
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• v.17 no.2
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• pp.265-273
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• 2001

In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.759-767
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• 2011

An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. A ring is strongly nil clean in case each of its elements is strongly nil clean. We investigate, in this article, the strongly nil cleanness of 2${\times}$2 matrices over local rings. For commutative local rings, we characterize strongly nil cleanness in terms of solvability of quadratic equations. The strongly nil cleanness of a single triangular matrix is studied as well.

• East Asian mathematical journal
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• v.27 no.5
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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.

• 한국초전도학회:학술대회논문집
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• v.13
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• pp.9-9
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• 2003

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.319-331
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• 2006

In this paper, a new class of general strongly nonlinear variational-like inequalities was introduced and studied. The existence and uniqueness of solutions and a new iterative algorithm for the general strongly nonlinear variational-like inequality are established and suggested, respectively. The convergence criteria of the iterative sequence generated by the iterative algorithm are also given.