It is known that a uniformly convex Banach space is reflexive and strictly convex. E is said to be smooth provided limt→ ‖x+ty‖–‖x‖ t exists for all x, y ∈UE . It is also said to be uniformly smooth if the limit is attained uniformly for all x, y ∈UE . It is well known that if E* is strictly convex, then J is single valued; if E* is reflexive, and smooth, then J is single valued and demicontin...

We analyze the asymptotic behavior of infinite products non-linear operators which take a non-empty, closed subset complete metric space into space, taking account summable computational errors. Our results can be applied in methods for solving convex feasibility and optimization problems.

In this paper we generalize to unbounded convex subsets C of hyperbolic spaces results obtained by W.A. Kirk and R. Esṕınola on approximate fixed points of nonexpansive mappings in product spaces (C×M)∞, where M is a metric space and C is a nonempty, convex, closed and bounded subset of a normed or a CAT(0)-space. We extend the results further, to families (Cu)u∈M of unbounded convex subsets of...

It is known that a Fréchet space F can be realized as a projective limit of a sequence of Banach spaces Ei. The space Kc(F) of all compact, convex subsets of a Fréchet space, F, is realized as a projective limit of the semilinear metric spacesKc(E). Using the notion of Hukuhara derivative for maps with values inKc(F), we prove the local and global existence theorems for an initial value problem...

In this paper, we show that a closed convex set C of a Banach space is strongly proximinal (proximinal, resp.) in every Banach space isometrically containing it if and only if C is locally (weakly, resp.) compact. As a consequence, it is proved that local compactness of C is also equivalent to that for every Banach space Y isometrically containing it, the metric projection from Y to C is nonemp...

Kinodynamic planning algorithms like RapidlyExploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, non-convex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow efficiently in systems with dynamics or differential constraints when using conventional proximity met...

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

In this paper, a new iteration scheme in uniformly convex metric space is defined and its convergence obtained. A numerical example also considered to compare the rate of convergences with that an existing scheme.

In the present paper, we introduces the notion of integral type contractive mapping with respect to ordered S-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered S-metric space. Moreover, we give an example to support our main result.