Inverse Strongly Monotone
Some results on approximate solutions of variational inequality problems for inverse strongly monotone operators
... Finally, the following theorem due to Yamada [] is connected with Theorem .. Theorem . Let C be a bounded subset of a Hilbert space H and S be a nonexpansive mapping of H into C. Let A be an injective operator ...
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An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces
... The set of solutions of the variational inequality problem is denoted by V IC, A. Such a problem is connected with the convex minimization problem, the complementarity problem, the problem of finding a point u ∈ E ...
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Convergence of Iterative Sequences for Generalized Equilibrium Problems Involving Inverse Strongly Monotone Mappings
... Corollary 2.3. Let C be a nonempty closed convex subset of a real Hilbert space H. Let F be a bifunction from C × C to R which satisfies (A1)–(A4). Let A : C → H be an α-inverse-strongly monotone ...
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A new algorithm for variational inequality problems with alpha-inverse strongly monotone maps and common fixed points for a countable family of relatively weak nonexpansive maps, with applications
... Theorem 5.3. Let E be a 2-uniformly convex and uniformly smooth real Banach space with dual space E ∗ . Let C be a nonempty closed and convex subset of E, and let A : C → E ∗ be an α -inverse strongly ...
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Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces
... 1/2-inverse strongly monotone, the problem of finding an element of V IK, A ∩ FT, where FT denotes the set of fixed points of the nonexpansive mapping T, is equivalent to that of finding an element ...
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A General Iterative Approach to Variational Inequality Problems and Optimization Problems
... an inverse-strongly monotone mapping and the set of fixed points of a nonexapansive mapping and then prove that the sequence generated by the proposed iterative scheme converges strongly to a ...
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Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities
... Our purpose in this paper is to introduce this general iterative algorithm for approxi- mating a common element of the set of common fixed point of a semigroup of nonex- pansive mappings and the set of solutions of ...
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General iterative methods for generalized equilibrium problems and fixed point problems of k-strict pseudo-contractions
... Theorem . Let K be a nonempty closed convex subset of the Hilbert space H and F : K × K → R be a bi-function satisfying (A)-(A). Let A be an α-inverse strongly monotone mapping and B be a ...
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Strong convergence of a hybrid projection iterative algorithm for common solutions of operator equations and of inclusion problems
... maximal monotone operator and an inverse-strongly monotone mapping, solutions of a monotone variational inequality, and fixed points of a strict pseudocontraction are ...
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Regularization method for Noor’s variational inequality problem induced by a hemicontinuous monotone operator
... -inverse strongly monotone mapping is a nonex- pansive ...-inverse strongly monotone mapping (see [, ...the inverse strongly ...
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Regularization and iterative method for general variational inequality problem in hilbert spaces
... of solution to the problem (1.2). Observe that, if T =: 0, the zero operator, then the problem (1.2) reduces to (1.1). Moreover, we would also like to notice that although many authors have proven results for finding the ...
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A modified regularization method for finding zeros of monotone operators in Hilbert spaces
... where F : H → R is a convex and differentiable function and G : H → R is a convex func- tion. It is well known that if ∇F is (/L)-Lipschitz continuous, then it is L-inverse strongly monotone []. ...
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ℵ1 directed inverse systems of continuous images of arcs
... Remark 2.5. Let us observe that Theorem 2.4 is not true for σ -directed inverse system. This is shown by an example of Nikiel [14, Example 4.3]. The sufficient and necessary condition for the limit of σ -directed ...
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Solution sensitivity of generalized nonlinear parametric (A,η,m) proximal operator system of equations in Hilbert spaces
... involving strongly monotone and relaxed cocoercive map- pings under suitable second order and regularity assumptions is an increasing interest, there are many motivated researchers basing their work on the ...
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Iterative methods for finding the minimum norm solution of the standard monotone variational inequality problems with applications in Hilbert spaces
... the monotone variational in- equality problem and prove that our algorithms converge strongly to the minimum-norm solution of variational inequality problem ...
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Approximate solutions to variational inequality over the fixed point set of a strongly nonexpansive mapping
... a monotone, hemicontinuous operator over the fixed point set of a strongly nonexpansive mapping on a real Hilbert ...the strongly nonexpansive mapping at each iteration, for solving the ...
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On multivalued nonlinear variational inclusion problems with accretive mappings in Banach spaces
... generalized monotone operators (named H-monotone operators), A-monotone opera- tors, (H ,η)-monotone operators in Hilbert spaces, H -accretive operators, generalized m- accretive mappings and ...
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Hybrid Steepest-Descent Methods for Solving Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators
... Let H be a real Hilbert space and let F : H → H be a boundedly Lipschitzian and strongly monotone operator. We design three hybrid steepest descent algorithms for solving variational inequality VIC, F of ...
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Implicit and explicit iterative algorithms for hierarchical variational inequality in uniformly smooth Banach spaces
... The purpose of this paper is to solve the hierarchical variational inequality with the constraint of a general system of variational inequalities in a uniformly convex and 2-uniformly smooth Banach space. We introduce ...
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A construction of a maximal monotone extension of a monotone map
... Any monotone map has a maximal monotone ...maximal monotone extension of a monotone map, and thereby we obtain a constructive proof of the ...maximal monotone extensions used in the ...
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