A fixed point theorem for JS-contraction type mappings with applications to polynomial approximations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4969-4978 ◽  
Author(s):  
Ishak Altun ◽  
Arifi Al ◽  
Mohamed Jleli ◽  
Aref Lashine ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Stancu Operators ◽  
Polynomial Approximations ◽  
New Class ◽  
Contraction Type ◽  
Linear And Nonlinear

A fixed point theorem is established for a new class of JS-contraction type mappings. As applications, some Kelisky-Rivlin type results are obtained for linear and nonlinear q-Bernstein-Stancu operators.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

scholarly journals On the controllability of fractional dynamical systems

2012 ◽  
Vol 22 (3) ◽  
pp. 523-531 ◽  
Author(s):  
Krishnan Balachandran ◽  
Jayakumar Kokila
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Matrix Function ◽  
Sufficient Conditions ◽  
Schauder’S Fixed Point Theorem ◽  
Finite Dimensional ◽  
Linear And Nonlinear ◽  
Controllability Grammian

Abstract This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

scholarly journals ORBITALLY NONEXPANSIVE MAPPINGS

2015 ◽  
Vol 93 (3) ◽  
pp. 497-503 ◽  
Author(s):  
ENRIQUE LLORENS-FUSTER
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
New Class ◽  
Nonlinear Mappings

We define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.

Some fixed point theorems in partial \(S_b\)-metric spaces

2018 ◽  
Vol 9 (1) ◽  
pp. 1
Author(s):  
Koushik Sarkar ◽  
Manoranjan Singha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
New Class ◽  
Contractive Mappings ◽  
Banach Contraction

N. Souayah [10] introduced the concept of partial Sb-metric spaces. In this paper, we established a fixed point theorem for a new class of contractive mappings and a generalization of Theorem 2 from [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Am. Math. Soc. 136, (2008), 1861-1869] in partial Sb-metric spaces. We provide an example in support of our result.

scholarly journals Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Pengju Duan ◽  
Min Ren ◽  
Shilong Fei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Brownian Motions ◽  
Snell Envelope ◽  
New Class

This paper deals with a new class of reflected backward stochastic differential equations driven by countable Brownian motions. The existence and uniqueness of the RBSDEs are obtained via Snell envelope and fixed point theorem.

scholarly journals A Generalization of a Greguš Fixed Point Theorem in Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Marwan A. Kutbi ◽  
A. Amini-Harandi ◽  
N. Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
New Class ◽  
Contractive Mappings

We first introduce a new class of contractive mappings in the setting of metric spaces and then we present certain Greguš type fixed point theorems for such mappings. As an application, we derive certain Greguš type common fixed theorems. Our results extend Greguš fixed point theorem in metric spaces and generalize and unify some related results in the literature. An example is also given to support our main result.

scholarly journals A Fixed-Point Theorem for Ordered Contraction-Type Decreasing Operators in Banach Space with Lattice Structure

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Chenguang Wang ◽  
Jinxiu Mao ◽  
Zengqin Zhao
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Iterative Algorithm ◽  
Point Theorem ◽  
Unique Fixed Point ◽  
Lattice Structure ◽  
Contraction Type

In this work, we mainly improve the results in Amini-Harandi and Emami (2010). By introducing a new kind of ordered contraction-type decreasing operator in Banach space, we obtain a unique fixed point by using the iterative algorithm. An example is also presented to illustrate the theorem.

scholarly journals On the approximation of fixed points for a new class of generalized Berinde mappings

2016 ◽  
Vol 32 (3) ◽  
pp. 363-374
Author(s):  
BESSEM SAMET ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
New Class ◽  
Contractive Type

In this paper, we introduce a new class of operators, for which a fixed point theorem is proven. This class of mappings is very large and unifies several classes of contractive type operators from the literature, including Berinde mappings. Such fact is proven via a comparison with various metrical contractive type mappings.

Best proximity point theorems for weak cyclic Bianchini contractions

2018 ◽  
Vol 27 (1) ◽  
pp. 71-78
Author(s):  
Mihaela Ancuţa Petric ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Best Proximity Point ◽  
Type Theorem ◽  
Best Proximity Points ◽  
New Class ◽  
Point Type

Following the technique introduced in [Eldred, A. A. and Veeramani, P., Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001–1006], in this paper we will extend Bianchini’s fixed point theorem to best proximity point type theorem. We introduce a new class of contractive conditions, called weak cyclic Bianchini contractions.

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