• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.71-84
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• 2013

In this paper we study some nonlinear Pachpatte type integral inequalities on time scales by using a Bihari type inequality. Our results unify some continuous inequalities and their corresponding discrete analogues, and extend these inequalities to dynamic inequalities on time scales. Furthermore, we give some examples concerning our results.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.165-172
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• 2003

In this paper, we introduce the concept of well-posedness for general variational inequalities and obtain some results under pseudomonotonicity. It is well known that monotonicity implies pseudomonotonicity, but the converse is not true. In this respect, our results represent an improvement and refinement of the previous known results. Since the general variational inequalities include (quasi) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems.

• East Asian mathematical journal
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• v.18 no.1
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• pp.95-109
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• 2002

In this paper, we study a class of variational inequalities, which is called the generalized set-valued mixed variational inequality. By using the properties of the resolvent operator associated with a maximal monotone mapping in Hilbert spaces, we have established an existence theorem of solutions for generalized set-valued mixed variational inequalities, suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized set-valued mixed variational inequalities.

• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.63-78
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• 2011

In the present paper, we obtain integral inequalities involving the Kurzweil-Stieltjes integrals which generalize Gronwall-Bellman inequality and we use the inequalities to verify existence of solutions of a certain integral equation. Such inequalities will play an important role in the study of impulsively perturbed systems [9].

• Honam Mathematical Journal
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• v.44 no.2
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• pp.244-258
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• 2022

In this work, by using an integral identity together with both the Hölder and the power-mean integral inequalities we establish several new inequalities for n-times differentiable arithmetic-harmonically-convex function. Then, using this inequalities, we obtain some new inequalities connected with means. In special cases, the results obtained coincide with the well-known results in the literature.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.285-299
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• 2023

In the present paper, we establish some perturbed Newton-type inequalities in the case of twice differentiable convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the aid of special cases of our main results, we also give some previously obtained Newton-type inequalities.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.341-356
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• 2024

In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.59-72
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• 2005

The auxiliary principle is used to suggest and analyze some iterative methods for solving solving hemivariational inequalities under mild conditions. The results obtained in this paper can be considered as a novel application of the auxiliary principle technique. Since hemivariational in­equalities include variational inequalities and nonlinear optimization problems as special cases, our results continue to hold for these problems.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.633-639
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• 2004

In this paper using integral representations for n-time differentiable mappings, we establish new generalizations of certain Ostrowski and Trapezoid type inequalities by using fairly elementary analysis.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.247-259
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• 2017

By the use of inequalities for nonnegative Hermitian forms some new inequalities for numerical radius of bounded linear operators in complex Hilbert spaces are established.