‎our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove a strong convergence theorem for approximating a solution of split equality fixed point problem for quasi-nonexpansive mappings in a real hilbert space‎. ‎so many have used algorithms involving the operator norm for solving split equality fixed point problem‎, ‎...

Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation du(t)/dt + Au(t)+ G(u)(t) f(t), where A is a maximal monotone operator in a nilbert space H,f E LI(0,:H) and G:C([O,c):D(A))LI(O,c:H)is a given mapping.

The purpose of this article is to investigate common solutions of a zero point problem of a accretive operator and a fixed point problem of a nonexpansive mapping via a viscosity approximation method involving a τ-contractive mapping. c ©2017 All rights reserved.

Let C be a subset of a Banach space E. A mapping T : C → E is nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖ for all x, y ∈ C. In 1965, it was proved independently by Browder 1 , Göhde 2 , and Kirk 3 that if C is a bounded closed convex subset of a Hilbert space and T : C → C is nonexpansive, then T has a fixed point. Combining the results above, Ray 4 obtained the following interesting result see 5 for a...

In this paper, we study the nonexpansive properties of a generalized forward–backward splitting (G-FBS) operator, particularly under setting degenerate metric, from which follow convergence results in terms metric associated fixed-point iterations. The descent lemma and sufficient decrease property are also extended to case. It is further shown that G-FBS operator provides simplifying unifying ...

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.

We prove some existence theorems for solutions of a certain system of multivariate nonexpansive operator equations and calculate the solutions by using the generalized Mann and Halpern iterative algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and extend the previously known ones in the literature.

Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and recovery are reducible to the basic task finding point closed convex subset Hilbert space satisfies number nonlinear equations involving firmly nonexpansive operators. We investigate this formalism case when, due inaccurate modeling or perturbations, inconsistent. A relaxed formulation ...

The common fixed point results for Banach operator pair with generalized nonexpansive mappings in q-normed space have been obtained in the present work. As application, some more general best approximation results have also been determined without the assumption of linearity or affinity of mappings. These results unify and generalize various existing known results with the aid of more general c...