Fixed point theory for cyclic -contractions

2010 ◽  
Vol 72 (3-4) ◽  
pp. 1181-1187 ◽  
Author(s):  
Mădălina Păcurar ◽  
Ioan A. Rus
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cyclic Contractions

Probabilistic p-cyclic contractions using different types of t-norms

2018 ◽  
Vol 26 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Samir Kumar Bhandari ◽  
Parbati Saha
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Optimization Problems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Third Order ◽  
Menger Space ◽  
Different Types ◽  
Cyclic Contractions ◽  
Probabilistic Metric

Abstract Cyclic mappings have appeared prominently in fixed point theory during the last decade. They have also their applications in global optimization problems. Note that p-cyclic mappings are extensions of cyclic mappings over p number of sets. In this paper we introduce two p-cyclic contractions in probabilistic spaces. We have two corresponding fixed point theorems using third-order Hadzic-type t-norm and minimum t-norm, respectively. One of the probabilistic contractions is of Ciric type while the other is a general contraction. One illustrative example is given. The space we consider here is a 2-Menger space which is an extension of a probabilistic metric space in the same vein as the 2-metric spaces are extensions of metric spaces.

scholarly journals An improvement result concerning fixed point theory for cyclic contractions

2016 ◽  
Vol 32 (3) ◽  
pp. 339-347
Author(s):  
MOHAMED JLELI ◽  
◽  
BESSEM SAMET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
System Of Functional Equations ◽  
Cyclic Contractions ◽  
Closure Assumption

In this note, we obtain an improvement result for cyclic contractions by weakening the closure assumption that is usually supposed in the literature. We present some applications of the obtained result to prove the existence of solutions for a system of functional equations.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

scholarly journals A new method in fixed point theory

1960 ◽  
Vol 34 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Richard G. Swan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Method

Applications of General Infimum Principles to Fixed-Point Theory and Game Theory

2007 ◽  
Vol 16 (4) ◽  
pp. 375-398 ◽  
Author(s):  
Władysław Kulpa ◽  
Andrzej Szymanski
Keyword(s):  
Game Theory ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory

scholarly journals New Contribution to the Advancement of Fixed Point Theory, Equilibrium Problems, and Optimization Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-1 ◽  
Author(s):  
Wei-Shih Du ◽  
Erdal Karapınar ◽  
Lai-Jiu Lin ◽  
Gue Myung Lee ◽  
Tamaki Tanaka
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Fixed Point Theory ◽  
Point Theory

scholarly journals LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ruofeng Rao ◽  
Zhilin Pu
Keyword(s):  
Fixed Point ◽  
Stability Criterion ◽  
High Efficiency ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Linear Matrix ◽  
The Matrix ◽  
Matrix Exponential Function ◽  
Takagi Sugeno ◽  
First Time

By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI-based stability criterion of a class of time-delay Takagi-Sugeno (T-S) fuzzy differential equations. To the best of our knowledge, it is the first time to obtain the LMI-based stability criterion derived by a fixed point theory. It is worth mentioning that LMI methods have high efficiency and other advantages in largescale engineering calculations. And the feasibility of LMI-based stability criterion can efficiently be computed and confirmed by computer Matlab LMI toolbox. At the end of this paper, a numerical example is presented to illustrate the effectiveness of the proposed methods.

scholarly journals Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Chakkrid Klin-eam ◽  
Cholatis Suanoom
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to Rouzkard and Imdad (2012). This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

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