Related papers: On proximal uniform normal structure and relativel…
We provide a few characterizations of a strictly convex Banach space. Using this we improve the main theorem of [Digar, Abhik; Kosuru, G. Sankara Raju; Cyclic uniform Lipschitzian mappings and proximal uniform normal structure. Ann. Funct.…
Given $A$ and $B$ two nonempty subsets in a metric space, a mapping $T : A \cup B \rightarrow A \cup B$ is relatively nonexpansive if $d(Tx,Ty) \leq d(x,y) \text{for every} x\in A, y\in B.$ A best proximity point for such a mapping is a…
The aim of this paper is to address an open problem given in [Kirk, W. A., Shahzad, Naseer, Normal structure and orbital fixed point conditions, J. Math. Anal. Appl. {\bf{vol 463(2)}}, (2018) 461--476]. We give a characterization of weak…
The purpose of this paper is to study an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth and uniformly convex Banach space with respect to a left regular sequence of means defined on an…
We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…
Let $(A, B)$ be a nonempty bounded closed convex proximal parallel pair in a nearly uniformly convex Banach space and $T: A\cup B \rightarrow A\cup B$ be a continuous and asymptotically relatively nonexpansive map. We prove that there…
In this paper, we present some common fixed point theorems for a commuting pair of mappings, including a generalized nonexpansive single valued mapping and a generalized nonexpansive multivalued mapping in strictly convex Banach spaces. The…
In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use…
In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence…
The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…
The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…
We study the relations between different notions of almost locally uniformly rotund points that appear in literature. We show that every non-reflexive Banach space admits an equivalent norm having a point in the corresponding unit sphere…
In this paper, by using admissible sets, we give some fixed point results for orbitally contractions which diminish the radius of invariant convex subsets and orbits. Furthermore, a characterization of the weak normal structure by the fixed…
It is well known in convex analysis that proximal mappings on Hilbert spaces are $1$-Lipschitz. In the present paper we show that proximal mappings on uniformly convex Banach spaces are uniformly continuous on bounded sets. Moreover, we…
A Banach space (or its norm) is said to have the diameter $2$ property (D$2$P in short) if every nonempty relatively weakly open subset of its closed unit ball has diameter $2$. We construct an equivalent norm on $L_1[0,1]$ which is weakly…
In this paper, we prove the strong convergence theorems for nearly nonexpansive mappings, using the modified Picard-Mann hybrid iteration process in the context of uniformly convex Banach space.
We propose a unifying general (i.e. not assuming the mapping to have any particular structure) view on the theory of regularity and clarify the relationships between the existing primal and dual quantitative sufficient and necessary…
In this paper, we use the concept of proximal quasi-normal structure (P. Q-N. S) to study the existence of best proximity points for cyclic mappings, cyclic contractions, relatively Kannan nonexpansive mappings, as well as for orbitally…
For two nonempty, closed, bounded and convex subsets $A$ and $B$ of a uniformly convex Banach space $X$ consider a mapping $T:(A \times B) \cup (B \times A) \rightarrow A \cup B$ satisfying $T(A,B) \subset B$ and $T(B, A) \subset A$. In…
We present a construction that enables one to find Banach spaces $X$ whose sets $NA(X)$ of norm attaining functionals do not contain two-dimensional subspaces and such that, consequently, $X$ does not contain proximinal subspaces of finite…