scholarly journals Bounded and positive solutions of discrete steady state equations

2000 ◽  
Vol 31 (2) ◽  
pp. 131-136
Author(s):  
Sui Sun Cheng ◽  
Rigoberto Medina
Keyword(s):  
Steady State ◽  
Positive Solutions ◽  
State Equation ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
State Equations ◽  
Monotone Method ◽  
Steady State Equation ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Existence of bounded and/or positive solutions of a discrete steady state equation are derived by means of the Banach contraction principle and also by a monotone method.

Fuzzy double controlled metric spaces and related results

2021 ◽  
Vol 40 (5) ◽  
pp. 9977-9985
Author(s):  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Salman Furqan ◽  
Choonkil Park
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Triangular Inequality ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M q ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M q ( x , y , t ) ∗ M q ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

On the Edelstein Contractive Mapping Theorem

1975 ◽  
Vol 18 (5) ◽  
pp. 675-678
Author(s):  
Ludvik Janos
Keyword(s):  
Topological Space ◽  
Compact Subset ◽  
Contractive Mapping ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
Point Set ◽  
The Banach Contraction Principle

AbstractLet X be a metrizable topological space and f:X→X a continuous selfmapping such that for every x ∈ X the sequence of iterates {fn(x)} converges. It is proved that under these conditions the following two statements are equivalent:1. There is a metrization of X relative to which f is contractive in the sense of Edelstein.2. For any nonempty f-invariant compact subset Y of X the intersection of all iterates fn(Y) is a one-point set. The relation between this type of contractivity and the Banach contraction principle is also discussed.

scholarly journals On a New Generalization of Banach Contraction Principle with Application

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 862 ◽  
Author(s):  
Hüseyin Işık ◽  
Babak Mohammadi ◽  
Mohammad Reza Haddadi ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Current Work ◽  
Fixed Point Result ◽  
Banach Contraction ◽  
The Banach Contraction Principle

The main purpose of the current work is to present firstly a new generalization of Caristi’s fixed point result and secondly the Banach contraction principle. An example and an application is given to show the usability of our results.

scholarly journals Fixed-Point Theorems for θ − ϕ -Contraction in Generalized Asymmetric Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
Hamza Saffaj ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In the last few decades, a lot of generalizations of the Banach contraction principle had been introduced. In this paper, we present the notion of θ -contraction and θ − ϕ -contraction in generalized asymmetric metric spaces to study the existence and uniqueness of the fixed point for them. We will also provide some illustrative examples. Our results improve many existing results.

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