This paper is concerned with a common element of the set of fixed point for an asymptotically pseudocontractive mapping in the intermediate sense and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a general iterative scheme based on the shrinking projection method, which extends and improves that of ...

and Applied Analysis 3 where A n = α n I + A for all n ≥ 0. In particular, if V ≡ 0, then (11) reduces to the following iterative scheme: x 0 = x ∈ C chosen arbitrarily, y n = P C (x n − ] n A n x n ) , z n = β n x n + γ n P C (x n − ] n A n y n ) + σ n TP C (x n − ] n A n y n ) , x n+1 = P C [λ n (1 − δ n ) γSx n + (I − λ n μF) z n ] , ∀n ≥ 0. (12) Further, if S = V, then (11) reduces to the f...

‎the purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex banach space which has a‎ ‎uniformly g^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...

‎The purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex Banach space which has a‎ ‎uniformly G^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...

Abstract In a real Hilbert space, let the VIP, GSVI, HVI, and CFPP denote variational inequality problem, general system of inequalities, hierarchical inequality, common fixed-point problem countable family uniformly Lipschitzian pseudocontractive mappings an asymptotically nonexpansive mapping, respectively. We design two Mann implicit composite subgradient extragradient algorithms with line-s...

Abstract The aim of this work is to establish fixed point results in ordered Hilbert spaces for monotone operators with a pseudocontractive property. We state versions Theorem 12 [F. E. Browder, W. V. Petryshyn, Construction points nonlinear mappings space, J. Math. Anal. Appl. 20 (1967), 197–228] and 2.1 [Berinde, Vasile. Weak strong convergence theorems the Krasnoselskij iterative algorithm c...

Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E∗. Let S {T s : 0 ≤ s < ∞} be a nonexpansive semigroup on E such that Fix S : ⋂t≥0Fix T t / ∅, and f is a contraction on E with coefficient 0 < α < 1. Let F be δ-strongly accretive and λ-strictly pseudocontractive with δ λ > 1 and γ a positive real number such that γ < 1/α 1 − √ 1 − δ...

The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings. It is well known that the asymptotically nonexpansive mappings is a proper subclass of the class of asymptotically pseudocontractive mappings. In the present...