scholarly journals Data Dependence, Strict Fixed Point Results, and Well-Posedness of Multivalued Weakly Picard Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Azhar Hussain ◽  
Ahsan Ali ◽  
Vahid Parvaneh ◽  
Hassen Aydi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorems ◽  
Data Dependence ◽  
Well Posedness ◽  
Strict Fixed Point ◽  
Simulation Functions

In this paper, we introduce the notion of s , r -contractive multivalued weakly Picard operators via simulation functions, named as Z s , r -contractions. We present some related fixed point theorems. We investigate data dependence and strict fixed point results. The well-posedness for such operators is also considered. Moreover, we generalize the results of Moţ and Petruşel. To show the usability of our results, we give some examples and an application to resolve a functional equation arising in dynamical systems.

scholarly journals Ample Spectrum Contractions and Related Fixed Point Theorems

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1033 ◽  
Author(s):  
Antonio Francisco Roldán López de Roldán López de Hierro ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Point Of View ◽  
Strict Inequality ◽  
Simple Condition ◽  
Auxiliary Functions ◽  
Simulation Functions ◽  
Contractive Maps ◽  
R Functions

Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R-functions, ( R , S ) -contractions and ( A , S ) -contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.

scholarly journals Fixed points of hesitant fuzzy set-valued maps with applications

2021 ◽  
Vol 13 (3) ◽  
pp. 711-726
Author(s):  
M.S. Shagari ◽  
A. Azam
Keyword(s):  
Functional Equation ◽  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Fuzzy Set ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Hesitant Fuzzy Set ◽  
Alpha Beta

In this paper, the notion of hesitant fuzzy fixed points is introduced. To this end, we define Suzuki-type $(\alpha,\beta)$-weak contractions in the framework of hesitant fuzzy set-valued maps, thereby establishing some corresponding fixed point theorems. The presented concept herein is an extension of fuzzy set-valued and multi-valued mappings in the corresponding literature. Examples are provided to support the assertions and generality of our obtained ideas. Moreover, one of our results is applied to investigate sufficient conditions for existence of a class of functional equation arising in dynamic programming.

scholarly journals Fixed point theorems for simulation functions in $\mbox{b}$-metric spaces via the $wt$-distance

2017 ◽  
Vol 18 (1) ◽  
pp. 91 ◽  
Author(s):  
Chirasak Mongkolkeha ◽  
Yeol Je Cho ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partially Ordered ◽  
Simulation Functions

The purpose of this article is to prove some fixed point theorems for simulation functions  in complete b-metric   spaces with partially ordered  by using wt-distance which introduced by   Hussain et al.  Also, we give some  examples to illustrate  our  main results.

scholarly journals Some Fixed Point Theorems on $b$-$\theta$-metric spaces via $b$-simulation Functions

2021 ◽  
Author(s):  
Esra DALAN YILDIRIM ◽  
Ayşegül ÇAKSU GÜLER ◽  
Oya Bedre ÖZBAKIR
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Simulation Functions

scholarly journals Fixed point theorems for generalized (beta-phi)-contractive pair of mappings using simulation functions

2021 ◽  
Vol 39 (6) ◽  
pp. 183-194
Author(s):  
Manoj Kumar ◽  
Rashmi Sharma
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
New Class ◽  
Simulation Functions

In this paper, our aim is to present a new class of generalized (beta-phi)-Z- contractive pair of mappings and we prove certain xed point theorems for a pair of mappings using this concept. Our results generalizes some xed point theorems in the literature. As an application some xed point theorems endowed with a partial order in metric spaces are also proved.

scholarly journals Existence, uniqueness, Ulam–Hyers–Rassias stability, well-posedness and data dependence property related to a fixed point problem in gamma-complete metric spaces with application to integral equations

2022 ◽  
Vol 27 (1) ◽  
pp. 121-141
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Sunirmal Kundu ◽  
Priyam Chakraborty
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Data Dependence ◽  
Point Problem ◽  
Well Posedness ◽  
Complete Metric Spaces ◽  
Continuity Assumption ◽  
Dependence Property ◽  
Rassias Stability

In this paper, we study a fixed point problem for certain rational contractions on γ-complete metric spaces. Uniqueness of the fixed point is obtained under additional conditions. The Ulam–Hyers–Rassias stability of the problem is investigated. Well-posedness of the problem and the data dependence property are also explored. There are several corollaries of the main result. Finally, our fixed point theorem is applied to solve a problem of integral equation. There is no continuity assumption on the mapping.

scholarly journals On the Periods of Parallel Dynamical Systems

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Juan A. Aledo ◽  
Luis G. Diaz ◽  
Silvia Martinez ◽  
Jose C. Valverde
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Periodic Orbits ◽  
Fixed Point Theorems ◽  
Evolution Operators ◽  
Global Evolution

In this work, we provide conditions to obtain fixed point theorems for parallel dynamical systems over graphs with (Boolean) maxterms and minterms as global evolution operators. In order to do that, we previously prove that periodic orbits of different periods cannot coexist, which implies that Sharkovsky’s order is not valid for this kind of dynamical systems.

scholarly journals New Fixed Point Results for Modified Contractions and Applications

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 660
Author(s):  
Hüseyİn Işık ◽  
Hassen Aydi ◽  
Mohd Salmi Md Noorani ◽  
Haitham Qawaqneh
Keyword(s):  
Functional Equation ◽  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Contractive Mapping ◽  
Graph Type ◽  
New Type

In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the results obtained, some new fixed point theorems are presented for graph-type contractions. Furthermore, sufficient conditions are discussed to ensure the existence underlying various approaches of a solution for a functional equation originating in dynamic programming.

scholarly journals A new approach to α-ψ-contractive mappings and generalized Ulam-Hyers stability, well-posedness and limit shadowing results

2015 ◽  
Vol 31 (3) ◽  
pp. 395-401
Author(s):  
WUTIPHOL SINTUNAVARAT ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Fixed Point Problems ◽  
Contractive Condition ◽  
Well Posedness ◽  
New Approach ◽  
Contractive Mappings ◽  
Admissible Mapping ◽  
Limit Shadowing

In this paper, we introduce the new concept of weakly α-admissible mapping and give example to show that our concept is different from the concept corresponding existing in the literature. We also establish fixed point theorems by using such concept along with α-ψ-contractive condition and give some example which support our main result while previous results in literature are not applicable. Moreover, we study the generalized UlamHyers stability, the well-posedness and the limit shadowing for fixed point problems satisfy our conditions.

scholarly journals Fixed Point Problems on Generalized Metric Spaces in Perov’s Sense

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 856
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota ◽  
Asim Naseem
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Data Dependence ◽  
Fixed Point Problems ◽  
Symmetry Condition ◽  
Point Problem ◽  
Well Posedness ◽  
Generalized Metric Spaces ◽  
Generalized Metric

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov’s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy–Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam–Hyers stability of the fixed point problem. An example is also given to sustain the presented results.

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