EXTREME POINTS OF CERTAIN BANACH SPACES RELATED TO CONDITIONAL EXPECTATIONS

On fixed points of fundamentally nonexpansive mappings in Banach spaces

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

Linear Functionals on Certain Banach Spaces

Common Fixed Points in Ordered Banach Spaces

In [1] Dhage, O’Regan and Agarwal introduced the class of weak isotone mappings and the class of countably condensing mappings in an ordered Banach space and they prove some common fixed point theorems for weak isotone mappings. In this paper we introduce the notion of g-weak isotone mappings which allows us to generalize some common fixed point theorems of [1]. We recall the definition of orde...

On Best Proximity Points in metric and Banach spaces

Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed...

New iteration process for approximating fixed points in Banach spaces

‎The object of this paper is to present a new iteration process‎. ‎We will show that our process is faster than the known recent iterative schemes‎. ‎We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings‎. ‎We also present a numerical example for proving the rate of convergence of our res...