scholarly journals The Existence of Solutions to Nonlinear Matrix Equations via Fixed Points of Multivalued F-Contractions

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 212 ◽  
Author(s):  
Nawab Hussain ◽  
Ghada Ali ◽  
Iram Iqbal ◽  
Bessem Samet
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Nonlinear Matrix Equation ◽  
Complete Metric Spaces ◽  
Nonlinear Matrix ◽  
Set Up ◽  
Proper Generalization ◽  
Adequate Condition ◽  
Do So

In this paper, we set up an adequate condition for the presence of a solution of the nonlinear matrix equation. To do so, we prove the existence of fixed points for multi-valued modified F-contractions in the context of complete metric spaces, which generalize, refine, and extend several existing results in the literature. An example is accompanies the obtained results to show that derived results are a proper generalization.

scholarly journals Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 93
Author(s):  
Zhenhua Ma ◽  
Azhar Hussain ◽  
Muhammad Adeel ◽  
Nawab Hussain ◽  
Ekrem Savas
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Positive Definite ◽  
Matrix Equations ◽  
Nonlinear Matrix Equation ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Positive Definite Solution ◽  
Nonlinear Matrix ◽  
Definite Solution

In this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + ∑ i = 1 m A i * γ ( X ) A i and give a numerical example.

scholarly journals Relation Theoretic (Θ,R) Contraction Results with Applications to Nonlinear Matrix Equations

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 767 ◽  
Author(s):  
Hamed Al-Sulami ◽  
Jamshaid Ahmad ◽  
Nawab Hussain ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Binary Relation ◽  
Metric Spaces ◽  
Matrix Equations ◽  
Existence Of A Solution ◽  
Complete Metric Spaces ◽  
Numerical Example ◽  
Nonlinear Matrix

Using the concept of binary relation R , we initiate a notion of Θ R -contraction and obtain some fixed point results for such mappings in the setting of complete metric spaces. Furthermore, we establish some new results of fixed points of N-order. Consequently, we improve and generalize the corresponding known fixed point results. As an application of our main result, we provide the existence of a solution for a class of nonlinear matrix equations. A numerical example is also presented to illustrate the theoretical findings.

scholarly journals Fixed points of Suzuki-type generalized multivalued (f,θ,L)- almost contractions with applications

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 499-518 ◽  
Author(s):  
Naeem Saleem ◽  
Mujahid Abbas ◽  
Basit Ali ◽  
Zahid Raza
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Almost Contraction ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Frame Work ◽  
Proper Generalization

In this paper, we define Suzuki type generalized multivalued almost contraction mappings and prove some related fixed point results. As an application, some coincidence and common fixed point results are obtained. The results proved herein extend the recent results on fixed points of Kikkawa Suzuki type and almost contraction mappings in the frame work of complete metric spaces. We provide examples to show that obtained results are proper generalization of comparable results in the existing literature. Some applications in homotopy, dynamic programming, integral equations and data dependence problems are also presented.

scholarly journals Fixed points of multivalued nonlinear F-contractions on complete metric spaces

2016 ◽  
Vol 21 (2) ◽  
pp. 201-210 ◽  
Author(s):  
Ishak Altun ◽  
Gülhan Mınak ◽  
Murat Olgun
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Maps ◽  
Famous Theorem ◽  
Complete Metric Spaces ◽  
Fixed Point Result ◽  
Proper Generalization

We introduce a new concept for multivalued maps, also called multivalued nonlinear F-contraction, and give a fixed point result. Our result is a proper generalization of some recent fixed point theorems including the famous theorem of Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334(1):132–139, 2007].

scholarly journals On New χ -Fixed Point Results for λ − Υ , χ -Contractions in Complete Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Babak Mohammadi ◽  
Wutiphol Sintunavarat ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Partial Metric ◽  
Nonlinear Integral Equations ◽  
Complete Metric Spaces ◽  
Partial Metric Spaces ◽  
Theoretical Results

The main aim of this work is to introduce the new concept of λ − Υ , χ -contraction self-mappings and prove the existence of χ -fixed points for such mappings in metric spaces. Our results generalize and improve some results in existing literature. Moreover, some fixed point results in partial metric spaces can be derived from our χ -fixed points results. Finally, the existence of solutions of nonlinear integral equations is investigated via the theoretical results in this work.

RANDOM COINCIDENCE AND FIXED POINTS FOR WEAKLY COMPATIBLE MAPPINGS IN CONVEX METRIC SPACES

2009 ◽  
Vol 02 (02) ◽  
pp. 171-182 ◽  
Author(s):  
Izmat Beg ◽  
Adnan Jahangir ◽  
Akbar Azam
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Coincidence Points ◽  
Random Coincidence ◽  
Complete Metric Spaces ◽  
Random Fixed Points ◽  
Weakly Compatible ◽  
Convex Metric Spaces

Some new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established. These results generalize some recent well known comparable results in the literature.

scholarly journals Some fixed point theorems on equivalent metric spaces

2021 ◽  
Vol 38 (1) ◽  
pp. 139-148
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
MARIANA CUFOIAN ◽  
ADRIANA MITRE
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Complete Metric Spaces

This paper aims to analyze the existence of fixed points for mappings defined on complete metric spaces satisfying almost contractive conditions and a general contractive inequality of integral type. The existence of a fixed point is ensured by hypotheses formulated in terms of equivalent metric spaces.

scholarly journals Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Poom Kumam ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Partial Metric ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Partial Metric Spaces

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

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