On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings

on intermediate value theorem in ordered banach spaces for noncompact and discontinuous mappings

in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

The Topological Degree for Noncompact Nonlinear Mappings in Banach Spaces

Let X and Y be Banach spaces, G an open subset of X. If we denote the closure of G by cl(G), let ƒ be a mapping of cl(G) into Y. For X~ Y and ƒ a compact mapping, Leray and Schauder [9] gave a definition of topological degree for mappings of the form ƒ —ƒ on the open set G over a point a of X whenever (I—f)"^) is a compact subset of G. The Leray-Schauder degree for compact displacements is the ...

Fixed Point Theorem for Discontinuous Mappings on Pn Spaces

We present a study on strong t-continuity and measure of discontinuity on PN spaces. As an application, we prove a fixed point theorem for a discontinuous self mapping on PN spaces by means of measure of discontinuity.

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Boundary value problems for linear operators in ordered Banach spaces

We study boundary value problems of the type Ax = r, φ(x) = φ(b) (φ ∈ M ⊆ E∗) in ordered Banach spaces. MSC classification (2000): 47A50, 47B60

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...