Browsing by Author "Vidya Sagar"

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An extragradient iterative scheme for common fixed point problems and variational inequality problems with applications
(Ovidius University, 2015) Petruşel Adrian; D.R. Sahu; Vidya Sagar
In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse strongly monotone mapping. We prove a strong convergence theorem for the sequences generated by this scheme and give some applications of our convergence theorem.
An extragradient iterative scheme for common fixed point problems and variational inequality problems with applications
(Sciendo, 2015) Adrian Petruşel; D.R. Sahu; Vidya Sagar
In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse strongly monotone mapping. We prove a strong convergence theorem for the sequences generated by this scheme and give some applications of our convergence theorem. © 2015 Sciendo. All rights reserved.
Approximation of common fixed points of a sequence of nearly nonexpansive mappings and solutions of variational inequality problems
(2012) D.R. Sahu; Shin Min Kang; Vidya Sagar
We introduce an explicit iterative scheme for computing a common fixed point of a sequence of nearly nonexpansive mappings defined on a closed convex subset of a real Hilbert space which is also a solution of a variational inequality problem. We prove a strong convergence theorem for a sequence generated by the considered iterative scheme under suitable conditions. Our strong convergence theorem extends and improves several corresponding results in the context of nearly nonexpansive mappings. Copyright © 2012 D. R. Sahu et al.
Iterative methods for hierarchical common fixed point problems and variational inequalities
(Springer International Publishing, 2013) D.R. Sahu; Shin Min Kang; Vidya Sagar
The purpose of this paper is to deal with the problem of finding hierarchically a common fixed point of a sequence of nearly nonexpansive self-mappings defined on a closed convex subset of a real Hilbert space which is also a solution of some particular variational inequality problem. We introduce two explicit iterative schemes and establish strong convergence results for sequences generated iteratively by the explicit schemes under suitable conditions. Our strong convergence results include the previous results as special cases, and can be viewed as an improvement and refinement of several corresponding known results for hierarchical variational inequality problems. ©#CPRSahu et al.; licensee Springer.
Iterative methods for triple hierarchical variational inequalities and common fixed point problems
(Springer International Publishing, 2014) D.R. Sahu; Shin Min Kang; Vidya Sagar; Satyendra Kumar
The purpose of this paper is to introduce a new iterative scheme for approximating the solution of a triple hierarchical variational inequality problem. Under some requirements on parameters, we study the convergence analysis of the proposed iterative scheme for the considered triple hierarchical variational inequality problem which is defined over the set of solutions of a variational inequality problem defined over the intersection of the set of common fixed points of a sequence of nearly nonexpansive mappings and the set of solutions of the classical variational inequality. Our strong convergence theorems extend and improve some known corresponding results in the contemporary literature for a wider class of nonexpansive type mappings in Hilbert spaces. MSC:47J20, 47J25. © 2014, Sahu et al.; licensee Springer.