A convexity in metric space and nonexpansive mappings. I.

APPROXIMATING COMMON FIXED POINTS OF A SEQUENCE OF ASYMPTOTICALLY QUASI-f-g-NONEXPANSIVE MAPPINGS IN CONVEX NORMED VECTOR SPACES

“…When we speak about metric properties in a normed vector space, we referring to this metric. It should be pointed out that each normed vector space is a special example of convex metric space, but there exist some convex metric spaces which can not be embedded into any normed spaces [5]. Now, we introduce a new implicit iteration process;…”

Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces

“…We note that a metric space which satisfies only condition (i), is consistent with a convex metric space, which was introduced by Takahashi [25]. Further, the concept of hyperbolic spaces in [9] is more restrictive than that introduced by Kuhfittig [11], because conditions (i)-(iii) together are equivalent to (X, d, W) being a space of hyperbolic type in [11].…”

On measure of non-compactness in convex metric spaces

“…Further, one can introduce a concept of convexity in metric space in abstract form and study the properties of such spaces -called convex metric spaces. At first it was done by W. Takahashi [3]. Definition 1.…”

“…Takahashi has shown ( [3]) that open and closed balls are convex, and that the arbirary intersection of convex sest is convex too.…”