• 제목/요약/키워드: equivalent inequality

검색결과 53건 처리시간 0.029초

THE EQUIVALENT FORM OF A MATRIX INEQUALITY AND ITS APPLICATION

  • ZHONGPENG YANG;XIAOXIA FENG
    • Journal of applied mathematics & informatics
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    • 제20권1_2호
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    • pp.421-431
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    • 2006
  • In this paper, we establish a matrix inequality and its equivalent form. Applying the results, some matrix inequalities involving Khatri-Rao products of positive semi-definite matrices are generalized.

MIXED QUASI VARIATIONAL INEQUALITIES INVOLVING FOUR NONLINEAR OPERATORS

  • Pervez, Amjad;Khan, Awais Gul;Noor, Muhammad Aslam;Noor, Khalida Inayat
    • 호남수학학술지
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    • 제42권1호
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    • pp.17-35
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    • 2020
  • In this paper we introduce and consider a new class of variational inequalities with four operators. This class is called the extended general mixed quasi variational inequality. We show that the extended general mixed quasi variational inequality is equivalent to the fixed point problem. We use this alternative equivalent formulation to discuss the existence of a solution of extended general mixed quasi variational inequality and also develop several iterative methods for solving extended general mixed quasi variational inequality and its variant forms. We consider the convergence analysis of the proposed iterative methods under appropriate conditions. We also introduce a new class of resolvent equation, which is called the extended general implicit resolvent equation and establish an equivalent relation between the extended general implicit resolvent equation and the extended general mixed quasi variational inequality. Some special cases are also discussed.

On an Extension of Hardy-Hilbert's Inequality

  • Yang, Bicheng
    • Kyungpook Mathematical Journal
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    • 제46권3호
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    • pp.425-431
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    • 2006
  • In this paper, by introducing three parameters A, B and ${\lambda}$, and estimating the weight coefficient, we give a new extension of Hardy-Hilbert's inequality with a best constant factor, involving the Beta function. As applications, we consider its equivalent inequality.

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On a Reverse Hardy-Hilbert's Inequality

  • Yang, Bicheng
    • Kyungpook Mathematical Journal
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    • 제47권3호
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    • pp.411-423
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    • 2007
  • This paper deals with a reverse Hardy-Hilbert's inequality with a best constant factor by introducing two parameters ${\lambda}$ and ${\alpha}$. We also consider the equivalent form and the analogue integral inequalities. Some particular results are given.

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On a Relation to Hilbert's Integral Inequality and a Hilbert-Type Inequality

  • Yang, Bicheng
    • Kyungpook Mathematical Journal
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    • 제49권3호
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    • pp.563-572
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    • 2009
  • In this paper, by introducing some parameters and using the way of weight function, a new integral inequality with a best constant factor is given, which is a relation between Hilbert's integral inequality and a Hilbert-type inequality. As applications, the equivalent form, the reverse forms and some particular inequalities are considered.

A New Dual Hardy-Hilbert's Inequality with some Parameters and its Reverse

  • Zhong, Wuyi
    • Kyungpook Mathematical Journal
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    • 제49권3호
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    • pp.493-506
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    • 2009
  • By using the improved Euler-Maclaurin summation formula and estimating the weight coefficients in this paper, a new dual Hardy-Hilbert's inequality and its reverse form are obtained, which are all with two pairs of conjugate exponents (p, q); (r, s) and a independent parameter ${\lambda}$. In addition, some equivalent forms of the inequalities are considered. We also prove that the constant factors in the new inequalities are all the best possible. As a particular case of our results, we obtain the reverse form of a famous Hardy-Hilbert's inequality.