scholarly journals Near-Fixed Point Results via Ƶ-Contractions in Metric Interval and Normed Interval Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2320
Author(s):  
Muhammad Sarwar ◽  
Misbah Ullah ◽  
Hassen Aydi ◽  
Manuel De La Sen
Keyword(s):  
Fixed Point ◽  
Simulation Functions

Wu (2018) proved near-fixed point results in metric interval and normed interval spaces. In this paper, generalizing his work, we proved near-fixed point results in these interval spaces using α—admissibility and the concept of simulation functions. The results have been proved using Z-contractions.

Fuzzy fixed point results via simulation functions

2021 ◽  
Author(s):  
Shehu Shagari Mohammed ◽  
Ibrahim Aliyu Fulatan
Keyword(s):  
Fixed Point ◽  
Simulation Functions ◽  
Fuzzy Fixed Point

Simulation functions and Meir–Keeler condensing operators with application to integral equations

2021 ◽  
Author(s):  
Moosa Gabeleh ◽  
Mehdi Asadi ◽  
Pradip Ramesh Patle
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Darbo’S Fixed Point Theorem ◽  
Simulation Functions ◽  
Condensing Operators

We propose a new concept of condensing operators by using a notion of measure of non-compactness in the setting of Banach spaces and establish a new generalization of Darbo’s fixed point theorem. We also show the applicability of our results to integral equations. A concrete example will be presented to support the application part.

scholarly journals Fixed point results for Suzuki Type Σ-contractions via simulation functions in modular b-metric spaces

2020 ◽  
Author(s):  
Mahpeyker ÖZTÜRK ◽  
Abdurrahman Buyukkaya
Keyword(s):  
Fixed Point ◽  
Graph Theory ◽  
Common Fixed Point ◽  
Homotopy Theory ◽  
Metric Spaces ◽  
Simulation Functions ◽  
Compatibility Property

This study aims to introduce Suzuki type Σcontraction mappings with simulation functions in the frame of modular b-metric spaces. Also, some coincidence and common fixed point results are obtained for four mappings using the weakly compatibility property that these results are the extensions and improvements of the existing literature. Finally, we also present two applications on graph theory and homotopy theory, which show applicability and validity of our results.

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 On ℋ-Simulation Functions and Fixed Point Results in the Setting of ωt-Distance Mappings with Application on Matrix Equations

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 837
Author(s):  
Anwar Bataihah ◽  
Wasfi Shatanawi ◽  
Tariq Qawasmeh ◽  
Raed Hatamleh
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Matrix Equations ◽  
Simulation Function ◽  
Simulation Functions

The concepts of b-metric spaces and ω t -distance mappings play a key role in solving various kinds of equations through fixed point theory in mathematics and other science. In this article, we study some fixed point results through these concepts. We introduce a new kind of function namely, H -simulation function which is used in this manuscript together with the notion of ω t -distance mappings to furnish for new contractions. Many fixed point results are proved based on these new contractions as well as some examples are introduced. Moreover, we introduce an application on matrix equations to focus on the importance of our work.

scholarly journals L -Simulation Functions over b -Metric-Like Spaces and Fractional Hybrid Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shimaa I. Moustafa ◽  
Ayman Shehata
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Unique Solution ◽  
Caputo Fractional Derivative ◽  
Multipoint Boundary Conditions ◽  
Simulation Functions ◽  
Hybrid Differential Equation ◽  
Hybrid Differential Equations

In this paper, we establish some fixed point results for α q s p -admissible mappings embedded in L -simulation functions in the context of b -metric-like spaces. As an application, we discuss the existence of a unique solution for fractional hybrid differential equation with multipoint boundary conditions via Caputo fractional derivative of order 1 < α ≤ 2 . Some examples and corollaries are also considered to illustrate the obtained results.

scholarly journals An alternative and easy approach to fixed point results via simulation functions

2017 ◽  
Vol 50 (1) ◽  
pp. 223-230 ◽  
Author(s):  
Stojan Radenovic ◽  
Francesca Vetro ◽  
Jelena Vujaković
Keyword(s):  
Fixed Point ◽  
Simulation Functions

Abstract We discuss, extend, improve and enrich results on simulation functions established by several authors. Furthermore, by using Lemma 2.1 of Radenovic et al. [Bull. Iran. Math. Soc., 2012, 38, 625],we get much shorter and nicer proofs than the corresponding ones in the existing literature.

scholarly journals On non-linear contractions via extended CF-simulation functions

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3731-3750 ◽  
Author(s):  
Ankush Chanda ◽  
Arslan Ansari ◽  
Lakshmi Dey ◽  
Bosko Damjanovic
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Simulation Function ◽  
Complete Metric Spaces ◽  
Auxiliary Functions ◽  
Non Linear ◽  
Simulation Functions

On grounds of the notion of simulation functions, in this manuscript, we bring in the concept of an extended CF-simulation function and conceive a few common fixed point results via such kind of contractions on complete metric spaces. These class of auxiliary functions generalize, improve and extend those of simulation functions, extended simulation functions and CF-simulation functions. However, as applications of the aforesaid results, we figure out some related consequences of it on the said spaces. Our findings are authenticated by the aid of some competent, non-trivial and constructive examples.

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