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In this paper, we introduce a general composite iterative algorithm for findinding a common element of the set of solutions of variational inequality problem for a hemicontinuous monotone mapping and the set of fixed points of a hemicontinuous pseudocontractive mapping in a Hilbert space. Under suitable control conditions, we establish strong convergence of the sequence generated by the proposed iterative algorithm to a common element of two sets, which is the unique solution of a certain variational inequality related to a boundedly Lipschitzian and strongly monotone mapping. As a consequence, we obtain the unique minimum-norm common point of two sets. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, we present a explicit viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorem of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider and analyze a general iterative method to approximate a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping, which is the unique solution for the variational inequality in real Hilbert spaces. Furthermore, under reasonable conditions, the sequence generated by the proposed iterative scheme converges strongly to a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping, which is a solution of a certain optimization problem related to a strongly positive linear operator. The results presented in this paper improve and extend the corresponding results reported by some authors recently. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the generalized viscosity implicit rules of one asymptotically nonexpansive mapping in Hilbert spaces. We obtain some strong convergence theorems under certain assumptions imposed on the parameters. We also apply our main results to solve mixed equilibrium problem in Hilbert spaces. A numerical example is also given to support our main results. The results obtained in this paper improve and extend many recent ones in this field. [ABSTRACT FROM AUTHOR]

In this paper, some strong and Δ-convergence results for Suzuki generalized nonexpansive mappings in the setting of complete CAT(0) spaces are proved. We are using newly introduced K* iteration process for approximation of fixed point. We also give an example to show the efficiency of the K* iteration process. Our results are exten- sion, improvement and generalization of many well known results in the literature of fixed point theory in CAT(0) spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of total asymp- totically nonexpansive mappings and to prove some Δ-convergence theorems of it- eration processes with errors to approximating a common fixed point for four total asymptotically nonexpansive mappings in hyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current lit- erature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iterative process for approximation of a common fixed point for a finite family of multi-valued Bregman relatively nonexpansive mappings with a solution of the split feasibility problems in p-uniformly convex and uniformly smooth Banach spaces. We prove the strong convergence theorems of the proposed iterative process in p-uniformly convex and uniformly smooth Banach spaces and present the numerical results to verify the efficiency and implementation of our results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new extragradient method with regularization for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in infinitedimensional Hilbert spaces, combining the regularization method and the technique of averaged operator, we prove the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ under mild conditions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a viscosity rule for common fixed points of two non-expansive mappings in Hilbert spaces. The strong convergence of this technique is proved under certain assumptions imposed on the sequence of parameters. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study a class of new two-step viscosity iteration methods for approximating fixed points of set-valued nonexpansive mappings in CAT(0) spaces. Here, the fixed point is unique solution of a variational inequality with a contraction mapping. Further, we prove strong convergence theorem of the two-step viscosity iterations with some general conditions in a complete CAT(0) space. The presented results improve and unify the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Alghamdi et al. [The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), Article ID 96, 9 pages] associated with Φ-hemicontractive mappings in a nonempty convex subset of an arbitrary Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we give a multivalued version of Picard-Mann hybrid iterative process of Khan [4] in Kohlenbach hyperbolic space. This process converges faster than all of Picard, Mann and Ishikawa iterative processes. By using an idea of Shahzad and Zegeye [8] which removes a restriction on the mapping and the method of direct construction of Cauchy sequence as illustrated by Song and Cho [9], we obtain strong and Δ-convergence theorems of this process for a multivalued mapping. Our results improve corresponding results of Shazad and Zegeye [8], Song and Cho [9] and many other in the contemporary literature in terms of faster iteration, more general space and weaker condition on mapping T. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a general iterative algorithm for finding a common element of the set of common fixed points of an finite family of nonexpansive mappings and the set of solutions of class of variational inequalities in uniformly convex and q-uniformly smooth Banach space. We prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the variational inequality under suitable conditions. Our result improves and extends the recent results announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new iterative algorithms (one implicit and one explicit) for finding a common point of the set of zeros of an accretive operator and the set of fixed points of a nonexpansive mapping in a real uniformly convex Banach space having a uniformly Gfiateaux differentiable norm. Then under suitable control conditions, we establish strong convergence of sequence generated by proposed algorithm to a common point of above two sets, which is a solution of a ceratin variational inequality. The main theorems develop and complement some well-known results in the literature. [ABSTRACT FROM AUTHOR]

The study of iterated contraction was initiated by Rheinboldt in 1969. The concept of iterated contraction proves to be very useful in the study of certain iterative process and has wide applicability. In this paper a brief introduction of iterated contraction maps is given and some fixed point results are discussed. [ABSTRACT FROM AUTHOR]