Journal of Mathematical Analysis and Applications, 2006
In this paper, we consider some classes of merit functions for general variational inequalities. ... more In this paper, we consider some classes of merit functions for general variational inequalities. Using these functions, we obtain error bounds for the solution of general variational inequalities under some mild conditions. Since the general variational inequalities include variational inequalities, quasivariational inequalities and complementarity problems as special cases, results proved in this paper hold for these problems. In this respect, results obtained in this paper represent a refinement of previously known results for classical variational inequalities.
In this paper, we introduce and consider the problem of finding zeroes of difference of two monot... more In this paper, we introduce and consider the problem of finding zeroes of difference of two monotone operators in a Hilbert space. Using the resolvent operator technique, we show that this problem is equivalent to the fixed point problem. This equivalence is used to suggest and analyze an iterative method for finding a zero of difference of two monotone operators.
In this paper, we introduce and study a new class of variational inequalities, which is called th... more In this paper, we introduce and study a new class of variational inequalities, which is called the general set-valued variational inequality. These variational inequalities include the previously known classes of variational inequalities as special cases. We use the projection technique and its variant forms to suggest a number of iterative alogrithms for solving the general set-valued variational inequalities and set-valued complementarity problems. We also discuss the convergence of these iterative algorithms
Journal of Mathematical Analysis and Applications, 1997
In this paper, we use the auxiliary principle technique to prove the existence of a solution of s... more In this paper, we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities, which are called the generalized mixed variational-like inequalities. This technique is used to analyze an iterative algorithm. Several special cases, which can be obtained from our main result, are also discussed.
In this paper, we use the resolvent operator and auxiliary principle techniques to suggest and an... more In this paper, we use the resolvent operator and auxiliary principle techniques to suggest and analyze several iterative algorithms for solving mixed quasi variational inequalities and related problems. We study the convergence criteria of these algorithms under mild conditions. We also study the global stability and existence of a unique solution of these quasi variational inequalities by using the dynamical systems approach. Our results represent refinement and improvement of the previously known results for variational inequalities.
Journal of Mathematical Analysis and Applications, 1999
In this paper, we develop the sensitivity analysis for quasi variational inclusions by using the ... more In this paper, we develop the sensitivity analysis for quasi variational inclusions by using the implicit resolvent equations technique without assuming the differentiability of the given data.
Journal of Mathematical Analysis and Applications, 2003
In this paper, we consider and analyze a new class of extragradient-type methods for solving gene... more In this paper, we consider and analyze a new class of extragradient-type methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is weaker condition than monotonicity. Our proof of convergence is very simple as compared with other methods. The proposed methods include several new and known methods as special cases. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems.
Journal of Mathematical Analysis and Applications, 2002
In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansi... more In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.
Journal of Mathematical Analysis and Applications, 2006
In this paper, we consider some classes of merit functions for general variational inequalities. ... more In this paper, we consider some classes of merit functions for general variational inequalities. Using these functions, we obtain error bounds for the solution of general variational inequalities under some mild conditions. Since the general variational inequalities include variational inequalities, quasivariational inequalities and complementarity problems as special cases, results proved in this paper hold for these problems. In this respect, results obtained in this paper represent a refinement of previously known results for classical variational inequalities.
In this paper, we introduce and consider the problem of finding zeroes of difference of two monot... more In this paper, we introduce and consider the problem of finding zeroes of difference of two monotone operators in a Hilbert space. Using the resolvent operator technique, we show that this problem is equivalent to the fixed point problem. This equivalence is used to suggest and analyze an iterative method for finding a zero of difference of two monotone operators.
In this paper, we introduce and study a new class of variational inequalities, which is called th... more In this paper, we introduce and study a new class of variational inequalities, which is called the general set-valued variational inequality. These variational inequalities include the previously known classes of variational inequalities as special cases. We use the projection technique and its variant forms to suggest a number of iterative alogrithms for solving the general set-valued variational inequalities and set-valued complementarity problems. We also discuss the convergence of these iterative algorithms
Journal of Mathematical Analysis and Applications, 1997
In this paper, we use the auxiliary principle technique to prove the existence of a solution of s... more In this paper, we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities, which are called the generalized mixed variational-like inequalities. This technique is used to analyze an iterative algorithm. Several special cases, which can be obtained from our main result, are also discussed.
In this paper, we use the resolvent operator and auxiliary principle techniques to suggest and an... more In this paper, we use the resolvent operator and auxiliary principle techniques to suggest and analyze several iterative algorithms for solving mixed quasi variational inequalities and related problems. We study the convergence criteria of these algorithms under mild conditions. We also study the global stability and existence of a unique solution of these quasi variational inequalities by using the dynamical systems approach. Our results represent refinement and improvement of the previously known results for variational inequalities.
Journal of Mathematical Analysis and Applications, 1999
In this paper, we develop the sensitivity analysis for quasi variational inclusions by using the ... more In this paper, we develop the sensitivity analysis for quasi variational inclusions by using the implicit resolvent equations technique without assuming the differentiability of the given data.
Journal of Mathematical Analysis and Applications, 2003
In this paper, we consider and analyze a new class of extragradient-type methods for solving gene... more In this paper, we consider and analyze a new class of extragradient-type methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is weaker condition than monotonicity. Our proof of convergence is very simple as compared with other methods. The proposed methods include several new and known methods as special cases. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems.
Journal of Mathematical Analysis and Applications, 2002
In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansi... more In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.
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