scholarly journals Order-Lipschitz mappings restricted with linear bounded mappings in normed vector spaces without normalities of involving cones via methods of upper and lower solutions

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6691-6698
Author(s):  
Shujun Jiang ◽  
Zhilong Li
Keyword(s):  
Fixed Point ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Upper And Lower Solutions ◽  
Vector Spaces ◽  
Normed Vector Space ◽  
Unique Existence ◽  
Lipschitz Mappings ◽  
Normed Vector

In this paper, without assuming the normalities of cones, we prove some new fixed point theorems of order-Lipschitz mappings restricted with linear bounded mappings in normed vector space in the framework of w-convergence via the method of upper and lower solutions. It is worth mentioning that the unique existence result of fixed points in this paper, presents a characterization of Picard-completeness of order-Lipschitz mappings.

scholarly journals Two fixed point theorems and invariant integrals

1974 ◽  
Vol 11 (1) ◽  
pp. 15-30 ◽  
Author(s):  
T.J. Cooper ◽  
J.H. Michael
Keyword(s):  
Fixed Point ◽  
Vector Space ◽  
Fixed Point Theorems ◽  
Normed Vector Space ◽  
Invariant Integrals ◽  
Lower Semi ◽  
Normed Vector

Two fixed point theorems for a subset C of a normed vector space X are established by using the concept of centre. These results differ from previous fixed point theorems in that X is assumed to have a topology T as well as a norm. The norm is required to be lower semi-continuous with respect to T and C is required to be convex, bounded with respect to the norm and compact with respect to T.

scholarly journals Convexity and boundedness relaxation for fixed point theorems in modular spaces

2021 ◽  
Vol 22 (1) ◽  
pp. 91
Author(s):  
Fatemeh Lael ◽  
Samira Shabanian
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Recent Trend ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Vector Spaces ◽  
Modular Spaces ◽  
Mathematical Problems ◽  
Normed Vector

<p>Although fixed point theorems in modular spaces have remarkably applied to a wide variety of mathematical problems, these theorems strongly depend on some assumptions which often do not hold in practice or can lead to their reformulations as particular problems in normed vector spaces. A recent trend of research has been dedicated to studying the fundamentals of fixed point theorems and relaxing their assumptions with the ambition of pushing the boundaries of fixed point theory in modular spaces further. In this paper, we focus on convexity and boundedness of modulars in fixed point results taken from the literature for contractive correspondence and single-valued mappings. To relax these two assumptions, we seek to identify the ties between modular and b-metric spaces. Afterwards we present an application to a particular form of integral inclusions to support our generalized version of Nadler’s theorem in modular spaces.</p>

scholarly journals Fixed point theorems on ordered vector spaces

2014 ◽  
Vol 2014 (1) ◽  
pp. 109 ◽  
Author(s):  
Jin Li ◽  
Cong Zhang ◽  
Qi Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Vector Spaces ◽  
Ordered Vector Spaces

Uniform Domains and Uniform Domain Decomposition Property in Real Normed Vector Spaces

2013 ◽  
Vol 113 (1) ◽  
pp. 128 ◽  
Author(s):  
M. Huang ◽  
X. Wang
Keyword(s):  
Vector Space ◽  
Domain Decomposition ◽  
Vector Spaces ◽  
Uniform Domain ◽  
Normed Vector Space ◽  
Decomposition Property ◽  
Uniform Domains ◽  
Normed Vector

Let $E$ be a real normed vector space with $\dim(E)\geq 2$, $D$ a proper subdomain of $E$. In this paper we characterize uniform domains in $E$ in terms of the uniform domain decomposition property. In addition, we discuss the relation between quasiballs and domains with the quasiball decomposition property in $\mathsf{R}^n$.

scholarly journals Fixed point theorems for metric spaces with a conical geodesic bicombing

2017 ◽  
Vol 38 (5) ◽  
pp. 1642-1657 ◽  
Author(s):  
GIULIANO BASSO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Probability Measures

We derive two fixed point theorems for a class of metric spaces that includes all Banach spaces and all complete Busemann spaces. We obtain our results by the use of a $1$-Lipschitz barycenter construction and an existence result for invariant Radon probability measures. Furthermore, we construct a bounded complete Busemann space that admits an isometry without fixed points.

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