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This paper provides a new hybrid-type shrinking projection method for strong convergence results in a Hilbert space. The paper continues - by utilizing the proposed hybrid algorithm - with a strong convergence towards an approximate common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two finite families of k-strict pseudo-contractions in a Hilbert space. Comparatively, our results improve and extend various results announced in the current literature. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the functional equation arising in dynamic programming of multistage decision processes f(x)=opty∈Dopt{p(x, y), q(x, y)f(a(x, y)), r(x, y)f(b(x, y)), s(x, y)f(c(x, y))} for all x ∈ S. A few iterative algorithms for solving the functional equation are suggested. The existence, uniqueness and iterative approximations of solutions for the functional equation are discussed in the Banach spaces BC(S) and B(S) and the complete metric space BB(S), respectively. The properties of solutions, nonnegative solutions, and nonpositive solutions and the convergence of iterative algorithms for the functional equation and other functional equations, which are special cases of the above functional equation, are investigated in the complete metric space BB(S), respectively. Eight nontrivial examples which dwell upon the importance of the results in this paper are also given. [ABSTRACT FROM AUTHOR]

In this paper, inspired by Hussain et al. (Fixed Point Theory Appl. 2015:17, ), we study a modified Mann method to approximate strongly fixed points of strict pseudo-contractive mappings. In (Hussain et al. in Fixed Point Theory Appl. 2015:17, ) it is shown that the same algorithm converges strongly to a fixed point of a nonexpansive mapping under suitable hypotheses on the coefficients. Here the assumptions on the coefficients are different, as well as the techniques of the proof. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid type method which consists of a resolvent operator technique and a generalized projection onto a moving half-space for approximating a zero of a maximal monotone mapping in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved. Our results extend and improve the recent ones announced by Zhang (Oper. Res. Lett. 40:564-567, 2012) and Wei and Zhou (Nonlinear Anal. 71:341-346, 2009). [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new viscosity approximation method by using the shrinking projection algorithm to approximate a common fixed point of a countable family of nonlinear mappings in a Banach space. Under quite mild assumptions, we establish the strong convergence of the sequence generated by the proposed algorithm and provide an affirmative answer to an open problem posed by Maingé (Comput. Math. Appl. 59:74-79, 2010) for quasi-nonexpansive mappings. In contrast with related processes, our method does not require any demiclosedness principle condition imposed on the involved operators belonging to the wide class of quasi-nonexpansive operators. As an application, we also introduce an iterative algorithm for finding a common element of the set of common fixed points of an infinite family of quasi-nonexpansive mappings and the set of solutions of a mixed equilibrium problem in a real Banach space. We prove a strong convergence theorem by using the proposed algorithm under some suitable conditions. Our results improve and generalize many known results in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose an explicit viscosity approximation method for finding a common element of the set of xed points of strict pseudo-contractions and of the set of solutions of variational inequalities with inverse-strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider algorithms for constructing n-terms approximations with nonnegative coefficients. The convergence theorem is proved for a “positive” analog of the Pure Greedy Algorithm. We establish a condition on the sequence of weakness coefficients which is sufficient for the convergence of the Positive Weak Greedy Algorithm. This condition is also necessary for the class of monotone sequences. [ABSTRACT FROM AUTHOR]