scholarly journals Dislocated quasi cone b-metric space over Banach algebra and contraction principles with application to functional equations

2019 ◽  
Vol 17 (1) ◽  
pp. 1065-1081
Author(s):  
Reny George ◽  
Hossam A. Nabwey ◽  
Jelena Vujaković ◽  
R. Rajagopalan ◽  
Selva Vinayagam
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Common Fixed Point ◽  
Metric Space ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Identical Pair ◽  
Common Fixed Point Theorems

Abstract In this paper we introduce dislocated and dislocated quasi version of a cone b-metric space over a Banach algebra as well as weak semi α-admissible and α-identical pair of mappings and prove common fixed point theorems for a pair of α-identical and weak α-admissible mappings in the aforesaid spaces. Our results are supported with suitable examples and an application to a system of m-tupled functional equations.

scholarly journals Common fixed point theorems on quasi-cone metric space over a divisible Banach algebra

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Andreea Fulga ◽  
Hojjat Afshari ◽  
Hadi Shojaat
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Cone Metric Space ◽  
The Self ◽  
Common Fixed Point Theorems ◽  
Cone Metric

AbstractIn this manuscript, we investigate the existence and uniqueness of a common fixed point for the self-mappings defined on quasi-cone metric space over a divisible Banach algebra via an auxiliary mapping ϕ.

scholarly journals Extraction new results of common fixed point theorems for $({T}, {\alpha }_{{s}}, {F})$-contraction of six mappings in a tripled b-metric space with an application of integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ghorban Khalilzadeh Ranjbar ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Solution ◽  
Type Integral ◽  
First Time ◽  
Common Fixed Point Theorems

Abstract The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$ α s -admissible, triangular partially triple weakly $\alpha _{s}$ α s -admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, we present a new model, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.

Coupled coincidence and coupled common fixed point theorems on a fuzzy metric space with a graph

2018 ◽  
Vol 34 (3) ◽  
pp. 417-424
Author(s):  
PHUMIN SUMALAI ◽  
◽  
POOM KUMAM ◽  
DHANANJAY GOPAL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Directed Graph ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric ◽  
Coupled Common Fixed Point ◽  
Common Fixed Point Theorems ◽  
Coupled Coincidence

Inspired by the work of Dakjum et al. [Eshi, D., Das, P. K. and Debnath, P., Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory Appl., 37 (2016), 1–14], we introduce a new class of G − f−contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph.

scholarly journals Fixed Point and Common Fixed Point Theorems on Ordered Cone b-Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sahar Mohammad Abusalim ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Common Fixed Point Theorems ◽  
Cone Metric

The concept of a cone b-metric space has been introduced recently as a generalization of a b-metric space and a cone metric space in 2011. The aim of this paper is to establish some fixed point and common fixed point theorems on ordered cone b-metric spaces. The proposed theorems expand and generalize several well-known comparable results in the literature to ordered cone b-metric spaces. Some supporting examples are given.

scholarly journals Tripled coincidence and common fixed point theorems for hybrid pair of mappings

2013 ◽  
Vol 22 (1) ◽  
pp. 53-64
Author(s):  
ABDUL RAHIM KHAN ◽  
◽  
MUJAHID ABBAS ◽  
BASIT ALI ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Tripled Fixed Point ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems

The tripled fixed point is a generalization of the well known concept of ”coupled fixed point”. In this paper, we establish tripled coincidence and tripled common fixed point theorems for a hybrid pair consisting of a multi-valued and a single valued mapping on a metric space. We give examples to illustrate our results.

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