A new three-step iterative algorithm for approximating the zero point of the sum of an infinite family ofm-accretive mappings and an infinite family ofμi-inversely strongly accretive mappings in a real q-uniformly smooth and uniformly convex Banach space is presented. The computational error in each step is being considered. A strong convergence theorem is proved by means of some new techniques...

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.

For the approximation of fixed points of a nonexpansive operator T in a uniformly convex Banach space E the convergence of the Mann-Toeplitz iteration x„+1 = a„T(x„) + (1 a„)xñ is studied. Strong convergence is established for a special class of operators T. Via regularization this result can be used for general nonexpansive operators, if E possesses a weakly sequentially continuous duality map...

Let X and Y be real Banach spaces, ƒ a mapping of X into 2, y0 an element of Y It is our object in the present discussion to present a new existence theory for solutions of the equation y0£f(x) which extends, sharpens, and simplifies the corresponding theory for X — Y and ƒ hypermaximal accretive. This new existence theory is founded in a very basic way upon the fixed point theory of self-mappi...

In this article, we present new inequalities for the numerical radius of sum two Hilbert space operators. These will enable us to obtain many generalizations and refinements some well known inequalities, including multiplicative behavior norm bounds. Among other applications, it is shown that if T accretive-dissipative, then 1/?2 ||T|| ? ?(T), where ?(?) ||?||denote usual operator norm, respect...