and Applied Analysis 3 where K and Q are nonempty closed convex subsets of the infinite-dimension real Hilbert spaces H1 and H2, respectively, and A is bounded linear mapping from H1 to H2. Equation 1.9 models many applied problems arising from image reconstructions and learning theory see, e.g., 4 . Someworks on the finite dimensional setting with relevant projectionmethods for solving image r...

In this paper the turnpike property is established for convex optimal control problems, involving undiscounted utility function and differential inclusions defined by multi-valued mapping having convex graph. Utility function is concave but not necessarily strictly concave. The turnpike theorem is proved under the main assumption that over any given line segment, either multi-valued mapping is ...

In this paper, we establish a weak convergence theorem and some strong convergence theorems of an explicit iteration process for a finite family of strictly asymptotically pseudo-contractive mappings in the intermediate sense and also establish a strong convergence theorem by a new hybrid method for above said iteration scheme and mappings in the setting of Hilbert spaces. AMS Mathematics Subje...

Abstract In this paper, we introduce a new iterative algorithm for approximating common solution of Split Hierarchical Monotone Variational Inclusion Problem (SHMVIP) and Fixed Point (FPP) k-strictly pseudocontractive mappings in real Hilbert spaces. Our proposed method converges strongly, does not require the estimation operator norm it is without imposing strict condition compactness; these m...

and Applied Analysis 3 In 2007, Marino and Xu 11 proved the following strong convergence theorem by using the hybrid projection method for a strict pseudocontraction. They defined a sequence as follows: x0 ∈ C chosen arbitrarily, yn αnxn 1 − αn Txn, Cn { z ∈ C : ∥∥yn − z ∥ ∥ 2 ‖xn − z‖ 1 − αn k − αn ‖xn − Txn‖ } , Qn {z ∈ C : 〈xn − z, x0 − xn〉 0}, xn 1 PCn∩Qn x0 , n 0, 1, 2, . . . , 1.5 They pr...

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fi...

Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let f : K → K a contractive mapping and T : K → K be a uniformly continuous pseudocontractive mapping with F T / ∅. Let {λn} ⊂ 0, 1/2 be a seq...

we study the convergence of the modified noor iterative scheme for the class of asymptotically pseudocontractive mappings in the intermediate sense which is not necessarily lipschitzian. our results improves, extends and unifies the results of schu [23] and qin {it et al.} [25].