In this paper we propose several modified hybrid projection methods for solving common solutions to variational inequality problems involving monotone and Lipschitz continuous operators. Based on differently constructed half-spaces, the proposed methods reduce the number of projections onto feasible sets as well as the number of values of operators needed to be computed. Strong convergence theorems are established under standard assumptions imposed on the operators. An extension of the proposed algorithm to a system of generalized equilibrium problems is considered and numerical experiments are also presented.

In this paper we propose two strongly convergent parallel hybrid iterative methods for finding a common element of the set of fixed points of a family of quasi φ-asymptotically nonexpansive mappings {F (S j )} N j=1 , the set of solutions of variational inequalities {V I(A i , C)} M i=1 and the set of solutions of equilibrium problems {EP (f k )} K k=1 in uniformly smooth and 2-uniformly convex Banach spaces. A numerical experiment is given to verify the efficiency of the proposed parallel algorithms.

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In this paper we study some novel parallel and sequential hybrid methods for finding a common fixed point of a finite family of asymptotically quasi φnonexpansive mappings. The results presented here modify and extend some previous results obtained by several authors.

In this paper we introduce two novel convolutions for the fractional Fourier transforms (FRFT), and prove natural algebraic properties of the corresponding multiplications such as commutativity, associativity and distributivity, which may be useful in signal processing and other types of applications. We analyze a consequent comparison with other known convolutions, and establish a necessary and sufficient conditions for the solvability of associated convolution equations of both the first and second kind in L 1 (R) and L 2 (R) spaces. An example satisfying the sufficient and necessary condition for the solvability of the equations is given at the end of the paper.

We study switched singular systems in discrete time and first highlight that in contrast to continuous time regularity of the corresponding matrix pairs is not sufficient to ensure a solution behavior which is causal with respect to the switching signal. With a suitable index-1 assumption for the whole switched system, we are able to define a one-stepmap which can be used to provide explicit solution formulas for general switching signals.

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a b s t r a c tThe main aim of this work is to consider integral equations of convolution type with the Toeplitz plus Hankel kernels firstly posed by Tsitsiklis and Levy (1981) [11]. By constructing eight new generalized convolutions for the finite Hartley transforms we obtain a necessary and sufficient condition for the solvability and unique explicit L 2 -solution of those equations. Thanks to this convolution approach the solvability condition obtained here is remarkably different from those in Tsitsiklis and Levy (1981) [11] and in other papers.