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Abstract  

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

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Summary  

To verify the universal validity of the ``two-sided'' monotonicity condition introduced in [4], we will apply it to include more classical examples. The present paper selects the L p convergence case for this purpose. Furthermore, Theorem 3 shows that our improvements are not trivial.

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<a name="abs1"/>Abstract??We prove three theorems for sequences of ? group bounded variation, which are analogues of the theorems proved earlier for monotone, or quasi-monotone sequences, or sequences of rest bounded variation.

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Stanojevic, V. B. , L 1 -convergence of Fourier series with complex quasimonotone coefficients, Proc. Amer. Math. Soc. 86 (1982), 241–247. MR 83j :42009 Stanojevic V. B. L

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In this paper we deal with elliptic systems with discontinuous nonlinearities. The discontinuous nonlinearities are assumed to satisfy quasimonotone conditions. We shall use the method of upper and lower solutions with fixed point theorems on increasing operators in ordered Banach spaces to show some existence theorems.

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Summary Five interesting theorems of Konyushkov giving estimations for the best approximation in terms of the coefficients of a Fourier series are generalized or extended to the cases when the monotone or quasi-monotone coefficients are replaced by sequences of rest bounded variation of coefficients.

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Summary  

Recently we extended some interesting theorems of Konyushkov giving estimations for the best approximation by the coefficients of the Fourier series of the function in question. We replaced the monotone or quasi-monotone coefficient sequences by coefficient sequences of rest bounded variation. In this note both notions are generalized for such coefficient sequences where certain restriction is given only in terms of the "rest variation" of the sequence.

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In this paper we consider different types of generalized cone-mono-tone maps: polarly C-monotone, strictly polarly C-monotone, strongly polarly C-monotone, polarly C-pseudomonotone, strictly polarly C-pseudomonotone and polarly C-quasimonotone maps, where C is a cone in a finite-dimensional space R m. We characterize these maps in the case when they are radially continuous with respect to the positive polar cone C + of the cone C, generalizing some well known results. In the obtained theorems we use first and higher-order lower Dini directional derivatives.

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