scholarly journals Common Fixed-Point Results in Ordered Left (Right) Quasi- b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Hemant Kumar Nashine ◽  
Sourav Shil ◽  
Hiranmoy Garai ◽  
Lakshmi Kanta Dey ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Ordered Sets ◽  
Nonlinear Matrix ◽  
Fractional Differential ◽  
Left And Right

We use the notions of left- and right-complete quasi- b -metric spaces and partial ordered sets to obtain a couple of common fixed-point results for strictly weakly isotone increasing mappings and relatively weakly increasing mappings, which satisfy a pair of almost generalized contractive conditions. To illustrate our results, throughout the paper, we give several relevant examples. Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.

scholarly journals Hybrid Multivalued Type Contraction Mappings in αK-Complete Partial b-Metric Spaces and Applications

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 86 ◽  
Author(s):  
Eskandar Ameer ◽  
Hassen Aydi ◽  
Muhammad Arshad ◽  
Habes Alsamir ◽  
Mohd Noorani
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Metric Spaces ◽  
Matrix Equations ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Nonlinear Matrix ◽  
Set Up ◽  
Type Contraction

In this paper, we initiate the notion of generalized multivalued ( α K * , Υ , Λ ) -contractions and provide some new common fixed point results in the class of α K -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.

scholarly journals Common Fixed Point Theorems in Metric Spaces with Applications

2018 ◽  
Vol 11 (4) ◽  
pp. 1177-1190
Author(s):  
Pushpendra Semwal
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
System Of Functional Equations ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper we investigate the existence and uniqueness of common fixed point theorems for certain contractive type of mappings. As an application the existence and uniqueness of common solutions for a system of functional equations arising in dynamic programming are discuss by using the our results.

scholarly journals Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations via Common Fixed-Point Techniques in Complex Valued Fuzzy Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Humaira ◽  
Muhammad Sarwar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Common Fixed Point ◽  
Fractional Differential Equations ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Complex Valued

The main purpose of this paper is to study the existence theorem for a common solution to a class of nonlinear three-point implicit boundary value problems of impulsive fractional differential equations. In this respect, we study the fuzzy version of some essential common fixed-point results from metric spaces in the newly introduced notion of complex valued fuzzy metric spaces. Also, we provide an illustrative example to demonstrate the validity of our derived results.

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 Common Fixed Points of Locally Contractive Mappings in Multiplicative Metric Spaces with Application

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Mujahid Abbas ◽  
Bashir Ali ◽  
Yusuf I. Suleiman
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Common Fixed Points ◽  
Closed Ball ◽  
Common Solution ◽  
Contractive Mappings ◽  
Multiplicative Metric Spaces

The aim of this paper is to present common fixed point results of quasi-weak commutative mappings on a closed ball in the framework of multiplicative metric spaces. Example is presented to support the result proved herein. We also study sufficient conditions for the existence of a common solution of multiplicative boundary value problem. Our results extend and improve various recent results in the existing literature.

scholarly journals Fixed Point Of Contractive Mappings Of Integral Type Over An S^{JS}- Metric Space

2021 ◽  
Vol 52 ◽  
Author(s):  
Kushal Roy ◽  
Mantu Saha ◽  
Ismat Beg
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Integral Type ◽  
Couple Fixed Point ◽  
Contractive Mappings

We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on an S^{JS}- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results.

scholarly journals Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 453 ◽  
Author(s):  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Nonlinear Contractions

We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction.

Binary relation for tripled fixed point theorem in metric spaces

2021 ◽  
Vol 39 (2) ◽  
pp. 9-26
Author(s):  
Animesh Gupta ◽  
Vandana Rai
Keyword(s):  
Fixed Point ◽  
Binary Relation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Positive Definite ◽  
Nonlinear Matrix Equation ◽  
Tripled Fixed Point ◽  
Contractivity Condition ◽  
Nonlinear Matrix

In this paper we present a new extension of tripled fixed point theorems in metric spaces endowed with a reflexive binary relation that is not necessarily neither transitive nor antisymmetric. The key feature in this tripled fixed point theorems is that the contractivity condition on the nonlinear map is only assumed to hold on elements that are comparable in the binary relation. Next on the basis of the tripled fixed point theorems, we prove the existence and uniqueness of positive definite solutions of a nonlinear matrix equation of type

scholarly journals Positive Solutions of Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. Caballero ◽  
I. Cabrera ◽  
K. Sadarangani
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Fractional Differential

We investigate the existence and uniqueness of positive solutions of the following nonlinear fractional differential equation with integral boundary value conditions, , , where , and is the Caputo fractional derivative and is a continuous function. Our analysis relies on a fixed point theorem in partially ordered sets. Moreover, we compare our results with others that appear in the literature.

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