In this paper, by using generalized viscosity mappings, we prove two strong convergence theorems for finding fixed points of a nonexpansive mapping which is also unique solution the variational inequality. Our results extend and improve recent ones announced some authors.

In this paper, we deal with the problem of finding a common fixed point of a family of relatively nonexpansive mappings. We, first of all, discuss the properties of strongly relatively nonexpansive mappings and show a strong convergence theorem for a sequence of relatively nonexpansive mappings under some conditions. Using this result, we obtain a strong convergence theorem for a finite family ...

In this paper, we modify the KF-iteration process into hyperbolic metric spaces where symmetry condition is satisfied and establish weak w2-stability data dependence results for contraction mappings. We also prove some Δ-convergence strong convergence theorems generalized (α,β)-nonexpansive type 1 Finally, offer a numerical example of mappings show that more effective than other iterations. Our...

In this paper, some fixed point theorems for nonexpansive mappings in partially ordered spherically complete ultrametric spaces are proved. In addition, we investigate the existence of fixed points for nonexpansive mappings in partially ordered non-Archimedean normed spaces. Finally, we give some examples to discuss the assumptions and support our results.

The class of strictly pseudo-contractive mappings is known to have more powerful applications than the nonexpansive in solving nonlinear equations such as inverse and equilibrium problems. Motivated by potency mappings, a generalized viscosity implicit algorithm constructed for finding their fixed points framework Banach spaces. strong convergence newly sequence point mapping obtained under som...

and Applied Analysis 3 Lemma 2.2 cf., 4 . Let D be a nonempty subset of a reflexive, strictly convex, and smooth Banach space E. Let R be a retraction from E onto D. Then R is sunny and generalized nonexpansive if and only if 〈 x − Rx, JRx − Jy ≥ 0, 2.2 for all x ∈ E and y ∈ D. A generalized resolvent Jr of a maximal monotone operator B ⊂ E∗ × E is defined by Jr I rBJ −1 for any real number r >...

‎The proximal point algorithm‎, ‎which is a well-known tool for finding‎ ‎minima of convex functions‎, ‎is generalized from the classical‎ ‎Hilbert space framework into a nonlinear setting‎, ‎namely‎, ‎geodesic‎ ‎metric spaces of nonpositive curvature‎. ‎In this paper we propose an‎  ‎iterative algorithm for finding the common element of the‎ ‎minimizers of a finite family of convex functions a...

In this paper, we construct a new iterative scheme by hybrid projection method and prove strong convergence theorems for approximation of a common element of set of common fixed points of an infinite family of asymptotically quasi-φ-nonexpansive mappings, set of solutions to a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a u...

We introduce a general implicit algorithm for finding a common element of‎ ‎the set of solutions of systems of equilibrium problems and the set of common fixed points‎ ‎of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎. ‎Then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the so...

The authors have obtained the following results: 1 the definition of uniformly closed countable family of nonlinear mappings, 2 strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, 3 two examples of uniformly closed countable families of nonlinear mappings and applications, 4 an...