We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.

We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings andmonotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inversestrongly monotone mappings, whic...

We prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework of CAT(0) spaces. Our results generalize, extend, and unify the corres...

In this paper, we consider a new class of generalized variational inequalities and a new class of generalized Wiener-Hopf equations involving set-valued and nonexpansive mappings in real Hilbert space. Using the projection technique, we show that the generalized variational inequalities are equivalent to the generalized Wiener-Hopf equations. Further, by using this alternative equivalence we su...

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

F(T) ̸ = 0. As an important generalization of nonexpansive mappings, the class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [1] in 1972, who proved that if K is a nonempty, closed, and convex subset of a real uniformly convex Banach space and T : K → K is an asymptotically nonexpansive mapping, then T has a fixed point. Since then, iterative techniques for approximat...

Abstract The aim of this article is to design a new iteration process for solving certain fixed-point problems. In particular, we prove weak and strong convergence theorems generalized nonexpansive mappings in the framework uniformly convex Banach spaces. addition, discuss stability solution under mild conditions. Further, provide some numerical examples indicate that proposed method works prop...

In this work, we establish new fixed point theorems for generalized Pata–Suzuki type contraction via α -admissible mapping in metric spaces and to prove some results such mappings. Moreover, give an example illustrate our main result. Consequently, the presented paper generalize improve corresponding of literature.

By principal motivation from the results of new iterative scheme that produces faster than K-iteration. In this article, we study generalized by a iteration to approximate fixed points contraction and Suzuki non-expansive mappings. We establish strong convergence mappings closed convex Banach space also deduce data dependent results. Furthermore, prove some weak theorems in sense mapping applyi...

In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of nonexpansive mappings and the set of solutions of generalized variational inequalities for a k-strict pseudo-contraction by relaxed extra-gradient methods. Strong convergence theorems are established in q-uniformly smooth Banach spaces.