scholarly journals Coupled fixed point theorem and t-stability for nonlinear contractive mappings in cone metric spaces over Banach algebras

2018 ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Contractive Mappings ◽  
Coupled Fixed Point Theorem ◽  
Cone Metric

scholarly journals Coupled Fixed-Point Theorems in Theta-Cone-Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Sahar Mohamed Ali Abou Bakr
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Underlying Space ◽  
Coupled Fixed Point Theorem ◽  
Cone Metric

This paper gives further generalizations of some well-known coupled fixed-point theorems. Specifically, Theorem 3 of the paper is the generalization of the Baskar–Lackshmikantham coupled fixed-point theorem, and Theorem 5 is the generalization of the Sahar Mohamed Ali Abou Bakr fixed-point theorem, where the underlying space is complete θ -cone-metric space.

scholarly journals Fixed Point Theorems in Complete Cone Metric Spaces over Banach Algebras

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Seong-Hoon Cho
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Weak Contraction ◽  
Cone Metric Spaces ◽  
Contraction Type ◽  
Cone Metric

The notion of C-class functions in Banach algebras is introduced. By using such concept, a new fixed point theorem is established. An example to illustrate main theorem is given. Finally, applications of our main result to cyclic mappings and weak contraction type mappings are given.

scholarly journals Pentagonal Cone b-metric Spaces over Banach Algebras and Fixed Point Theorem of Generalized Lipschitz Mapping

2018 ◽  
Vol 22 ◽  
pp. 01003 ◽  
Author(s):  
Abba Auwalu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Lipschitz Mapping ◽  
Banach Fixed Point Theorem ◽  
Cone Metric ◽  
Generalized Lipschitz Mapping

In this paper, we introduce the concept of pentagonal cone b-metric space over Banach algebras as a generalization of cone metric space over Banach algebras and many of its generalizations. Furthermore, we prove Banach fixed point theorem in such a space. Our result unify, complement and/or generalized some recent results in the papers [1–7], and many others. We provide some examples to elucidate the validity and superiority of our results.

scholarly journals The Existence of Cone Critical Point and Common Fixed Point with Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Critical Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonlinear Dynamical Systems ◽  
Cone Metric Spaces ◽  
Nonlinear Dynamical ◽  
Cone Metric

We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. We also obtain some fixed point theorems for weakly contractive maps in the setting of cone metric spaces and focus our research on the equivalence between scalar versions and vectorial versions of some results of fixed point and others.

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