scholarly journals Fixed point theorems in uniformly rotund metric spaces

1976 ◽  
Vol 14 (2) ◽  
pp. 181-192 ◽  
Author(s):  
John Staples
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Linear Structure ◽  
Uniform Convexity ◽  
Uniformly Convex ◽  
Underlying Space ◽  
Uniformly Convex Banach Spaces ◽  
Definition Of

In recent years fixed point theorems have been proved for non-expansive and similar mappings on uniformly convex Banach spaces. The only role the linear structure plays in the statement of these results occurs in the definition of uniform convexity. It is therefore natural to ask whether the results depend essentially on the linear structure, or whether an extension of the notion of uniform convexity to metric spaces would allow the hypothesis of linear structure on the underlying space to be removed.

scholarly journals Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces

1999 ◽  
Vol 22 (1) ◽  
pp. 119-129
Author(s):  
Balwant Singh Thakur ◽  
Jong Soo Jung
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Hardy Space ◽  
Banach Spaces ◽  
Sobolev Spaces ◽  
Fixed Point Theorems ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces

Fixed point theorems for generalized Lipschitzian semigroups are proved inp-uniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, inLpspaces, in Hardy spaceHp, and in Sobolev spacesHk,p, for1<p<∞andk≥0.

scholarly journals Optimal Approximate Solutions of Fixed Point Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
S. Sadiq Basha ◽  
N. Shahzad ◽  
R. Jeyaraj
Keyword(s):  
Fixed Point ◽  
Approximate Solution ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Approximate Solutions ◽  
Uniformly Convex ◽  
Optimal Approximate Solution ◽  
Uniformly Convex Banach Spaces

The main objective of this paper is to present some best proximity point theorems for K-cyclic mappings and C-cyclic mappings in the frameworks of metric spaces and uniformly convex Banach spaces, thereby furnishing an optimal approximate solution to the equations of the form where is a non-self mapping.

Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph

2018 ◽  
Vol 27 (1) ◽  
pp. 37-48
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
LASZLO BALOG ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Condition

In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions T : K ⊂ X → X that satisfy Rothe’s boundary condition T (∂K) ⊂ K.

scholarly journals Some related fixed point theorems for multivalued mappings on two metric spaces

2020 ◽  
Vol 12 (2) ◽  
pp. 392-400
Author(s):  
Ö. Biçer ◽  
M. Olgun ◽  
T. Alyildiz ◽  
I. Altun
Keyword(s):  
Fixed Point ◽  
Classical Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Compact Set ◽  
Complete Metric Spaces ◽  
Bounded Set ◽  
Contraction Type ◽  
Definition Of

The definition of related mappings was introduced by Fisher in 1981. He proved some theorems about the existence of fixed points of single valued mappings defined on two complete metric spaces and relations between these mappings. In this paper, we present some related fixed point results for multivalued mappings on two complete metric spaces. First we give a classical result which is an extension of the main result of Fisher to the multivalued case. Then considering the recent technique of Wardowski, we provide two related fixed point results for both compact set valued and closed bounded set valued mappings via $F$-contraction type conditions.

scholarly journals Some fixed point theorems in n-normed spaces

2020 ◽  
Vol 25 (3) ◽  
pp. 1-15 ◽  
Author(s):  
Hanan Sabah Lazam ◽  
Salwa Salman Abed
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Normed Space ◽  
Fixed Point Theorems ◽  
Normed Spaces ◽  
Weak Contraction ◽  
Contraction Mappings ◽  
Basic Properties ◽  
Definition Of

In this article, we recall the definition of a real n-normed space and some basic properties. fixed point theorems for types of Kannan, Chatterge, Zamfirescu, -Weak contraction and  - (,)-Weak contraction mappings in  Banach spaces.

scholarly journals On Some Fixed Point Results forH+-Type Contraction Mappings in Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Hemant Kumar Pathak ◽  
Rosana Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Contractive Mappings ◽  
Type Contraction

We prove some fixed point theorems forH+-type multivalued contractive mappings in the setting of Banach spaces and metric spaces. The results provided allow recovering different well-known results.

scholarly journals Common fixed point iterations for a class of multi-valued mappings in $$\mathbf {CAT}(0)$$ spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 681-690
Author(s):  
Khairul Saleh ◽  
Hafiz Fukhar-ud-din
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Fixed Point Iterations

Abstract In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of $$CAT\left( 0\right) $$ C A T 0 spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert spaces.

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