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In this paper, a new iterative scheme by hybrid projection method is proposed for a finite family of Bregman totally quasi-D-asymptotically nonexpansive mappings. Conditions ensuring strong convergence are imposed to common elements of set of common fixed points of the mappings and set of common solutions to a system of generalized mixed equilibrium problems in a reflexive Banach space. These results extend many important recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a new nonlinear mapping called demigeneralized in a Banach space. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common fixed point for a family of the new nonlinear mappings in a Banach space. We apply this result to obtain new strong convergence theorems in a Hilbert space and a Banach space, respectively. [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]

Abstract: Let and f be a continuous, strictly monotone real-valued function. The weighted quasi-arithmetic mean of two numbers a, b is defined by . Let be an real matrix and . We construct a function by for all . In this paper we show that has a unique fixed point . Moreover, it can be shown that for each the sequence , generated by the following iterative scheme: and for all , converges to the unique fixed point . Besides, some properties of the fixed point are derived. As an application, our results imply that the max-weighted quasi-arithmetic mean powers of any matrix are always convergent. The continuity of the function defined by is proposed as well. [Copyright &y& Elsevier]