scholarly journals Fixed Point Results of a General Class of Monotone Nonexpansive Mappings in Hyperbolic Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Rida Outass ◽  
Karim Chaira ◽  
El Miloudi Marhrani ◽  
Nour-eddine El Harmouchi
Keyword(s):  
Fixed Point ◽  
General Class ◽  
Iterative Process ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Hyperbolic Metric ◽  
Ordered Metric Spaces ◽  
New Class

In this paper, we introduce and study some properties of a new class of generalized monotone nonexpansive mappings in hyperbolic metric spaces. Further, we give some results on the convergence of the Mann iterative process for this class of mappings in hyperbolic ordered metric spaces with some interesting examples.

scholarly journals Approximation of Endpoints for α—Reich–Suzuki Nonexpansive Mappings in Hyperbolic Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1692
Author(s):  
Izhar Uddin ◽  
Sajan Aggarwal ◽  
Afrah A. N. Abdou
Keyword(s):  
Fixed Point ◽  
Convergence Analysis ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Hyperbolic Metric ◽  
Convergence Theorems ◽  
Hyperbolic Metric Space

The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving α—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong and Δ—convergence theorems in a hyperbolic metric space. Thus, our results generalize and improve many existing results.

scholarly journals A new class of generalized contraction using P-functions in ordered metric spaces

2015 ◽  
Vol 23 (2) ◽  
pp. 93-106
Author(s):  
Sana Hadj Amor ◽  
Erdal Karapınar ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Contraction ◽  
Ordered Metric Spaces ◽  
New Class

Abstract In this paper, we introduced and studied a new class of mappings in ordered metric spaces that is inspired from the concept of a P-function introduced in Chaipunya et. al. [10]. With our new class, we furnish fixed point theorems for continuous, noncontinuous, monotonic, and nonmonotonic mappings in various kinds of the ordering structures.

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 Theorems for Boyd-Wong-Type Contractions in Ordered Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hassen Aydi ◽  
Wasfi Shatanawi ◽  
Mihai Postolache ◽  
Zead Mustafa ◽  
Nedal Tahat
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered

We give some fixed point results using an ICS mapping and involving Boyd-Wong-type contractions in partially ordered metric spaces. Our results generalize, extend, and unify several well-known comparable theorems in the literature. Also, we present some examples to support our results.

scholarly journals Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces

2012 ◽  
Vol 44 (3) ◽  
pp. 233-251 ◽  
Author(s):  
Erdal KARAPINAR ◽  
Hassen AYDI ◽  
Zead MUSTAFA
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper, we prove tripledcoincidence and common fixed point theorems for $F: X\times X\times X\to X$ and $g:X\to X$ satisfying almost generalized contractions in partially ordered metric spaces. The presented results generalize the theorem of Berinde and Borcut Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal 74(15) (2011)4889--4897. Also, some examples are presented.

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