scholarly journals Multivalued self almost local contractions

2019 ◽  
Vol 57 (1) ◽  
pp. 122-138
Author(s):  
Monica Zakany
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Nonlinear Analysis ◽  
Existence And Uniqueness ◽  
Picard Iteration ◽  
New Class ◽  
Contractive Mappings ◽  
Local Contraction

Abstract We introduce a new class of contractive mappings: the almost local contractions, starting from the almost contractions presented by V. Berinde in [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration Nonlinear Analysis Forum 9 (2004) No.1, 43-53], and also from the concept of local contraction presented by Filipe Martins da Rocha and Vailakis in [V. Filipe Martins-da-Rocha, Y. Vailakis, Existence and uniqueness of a fixed point for local contractions, Econometrica, vol.78, No.3 (May, 2010) 1127-1141]. First of all, we present the notion of multivalued self almost contractions with many examples. The main results of this paper are given by the extension to the case of multivalued self almost local contractions.

scholarly journals Fixed Points of ModifiedF-Contractive Mappings in Complete Metric-Like Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Hamed H. Alsulami ◽  
Erdal Karapınar ◽  
Hossein Piri
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Related Literature ◽  
Contractive Mappings

We introduce the notion of modifiedF-contractive mappings in the setting of complete metric-like spaces and we investigate the existence and uniqueness of fixed point of such mappings. The presented results unify, extend, and improve several results in the related literature.

scholarly journals Fixed point results on θ-metric spaces via simulation functions

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3365-3375 ◽  
Author(s):  
Ankush Chanda ◽  
Bosko Damjanovic ◽  
Lakshmi Dey
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Recent Article ◽  
Metric Spaces ◽  
New Class ◽  
Simulation Functions

In a recent article, Khojasteh et al. introduced a new class of simulation functions, Z-contractions, with blending over known contractive conditions in the literature. Subsequently, in this paper, we extend and generalize the results in ?-metric context and we discuss some fixed point results in connection with existing ones. Also, we originate the notion of modified Z-contractions and explore the existence and uniqueness of fixed points of such functions on the said spaces. Finally we include examples to instantiate our main results.

scholarly journals Cyclic generalized φ-contractions in b-metric spaces and an application to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2047-2057 ◽  
Author(s):  
Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Problem ◽  
Contractive Mappings

We introduce the notion of cyclic generalized ?-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented.

scholarly journals A Fixed Point Theorem for Contractive Mappings with Nonlinear Combinations of Rational Expressions in b-Metric Spaces

2017 ◽  
Vol 58 (1) ◽  
pp. 29-46
Author(s):  
W. E. Barrera ◽  
J. R. Morales ◽  
E. M. Rojas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Distance Functions ◽  
Contractive Mappings ◽  
Altering Distance ◽  
Rational Expressions ◽  
Rational Type

AbstractIn this paper we discuss the existence and uniqueness of fixed points for mappings satisfying several (nonlinear-combinations) contractive inequalities of rational type controlled by altering distance functions. Our results extend several fixed point results in the literature.

scholarly journals Fixed Point Results for Almost Generalized Cyclic(ψ,φ)-Weak Contractive Type Mappings with Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equations ◽  
Contractive Mappings ◽  
Contractive Type

We define a class of almost generalized cyclic(ψ,ϕ)-weak contractive mappings and discuss the existence and uniqueness of fixed points for such mappings. We present some examples to illustrate our results. Moreover, we state some applications of our main results in nonlinear integral equations.

Fixed point theorems of (α,ψ) G-contractive mappings in quasi-partial b-metric-like spaces endowed with a graph

2019 ◽  
pp. 2150014
Author(s):  
Anuradha Gupta ◽  
Manu Rohilla
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contractive Mappings

The notion of [Formula: see text] G-contractive mappings is defined and the existence and uniqueness of fixed points of such mappings on quasi-partial b-metric-like spaces endowed with a graph are obtained. An application and examples are provided to illustrate the results.

scholarly journals Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1594
Author(s):  
Antonio Francisco Roldán López de Hierro ◽  
Andreea Fulga ◽  
Erdal Karapınar ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Complete Metric Spaces ◽  
Auxiliary Functions ◽  
Fuzzy Metric ◽  
New Class

Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces.

Fuzzy Θf-contractive mappings and their fixed points with applications

2020 ◽  
Vol 39 (5) ◽  
pp. 7097-7106
Author(s):  
Hayel Nasr Saleh ◽  
Mohammad Imdad ◽  
Idrees Khan ◽  
Md Hasanuzzaman
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Present Article ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Auxiliary Function ◽  
Fuzzy Metric Spaces ◽  
New Class ◽  
Contractive Mappings

In the present article, inspired by the work of Jleli et al. [J. Inequal. Appl. 2014, 38 (2014)] and [J. Inequal. Appl. 2014, 439 (2014)] in metric spaces, we proposed a new class of contractive mappings termed as: fuzzy Θf-contractive mappings by using an auxiliary function Θf : (0, 1) → (0, 1) satisfying suitable properties. This class has further been weakened by defining the class of fuzzy Θf-weak contractive mappings to realize yet another class of contractive mappings. Thereafter, these two newly introduced classes of contractive mappings are utilized to establish some fixed point theorems in M-complete fuzzy metric spaces (in the sense of George and Veeramani). In support of our newly obtained results, we provide some examples besides furnishing applications to dynamic programming.

scholarly journals Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Marin Borcut ◽  
Mădălina Păcurar ◽  
Vasile Berinde
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Tripled Fixed Point ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Nonlinear Mappings

We present new results on the existence and uniqueness of tripled fixed points for nonlinear mappings in partially ordered complete metric spaces that extend the results in the previous works: Berinde and Borcut, 2011, Borcut and Berinde, 2012, and Borcut, 2012. An example and an application to support our new results are also included in the paper.

scholarly journals On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

2021 ◽  
Author(s):  
Mohammad Hussein Mohammad Rashid
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Random Operator ◽  
Random Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings

Abstract In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

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