scholarly journals Several Fixed Point Theorems in Convex b-Metric Spaces and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 242 ◽  
Author(s):  
Lili Chen ◽  
Chaobo Li ◽  
Radoslaw Kaczmarek ◽  
Yanfeng Zhao
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Iteration Scheme ◽  
Linear Integral Equation ◽  
Iteration Algorithm ◽  
Linear Integral ◽  
Mann’S Iteration

Our paper is devoted to indicating a way of generalizing Mann’s iteration algorithm and a series of fixed point results in the framework of b-metric spaces. First, the concept of a convex b-metric space by means of a convex structure is introduced and Mann’s iteration algorithm is extended to this space. Next, by the help of Mann’s iteration scheme, strong convergence theorems for two types of contraction mappings in convex b-metric spaces are obtained. Some examples supporting our main results are also presented. Moreover, the problem of the T-stability of Mann’s iteration procedure for the above mappings in complete convex b-metric spaces is considered. As an application, we apply our main result to approximating the solution of the Fredholm linear integral equation.

scholarly journals The Newtonian Operator and Global Convergence Balls for Newton’s Method

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1074
Author(s):  
José A. Ezquerro ◽  
Miguel A. Hernández-Verón
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Convergence ◽  
Point Theorem ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Integral Equation ◽  
The Fixed Point Theorem ◽  
Linear Integral

We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.

scholarly journals Some Fixed-Point Theorems in b-Dislocated Metric Space and Applications

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 691 ◽  
Author(s):  
Panda Sumati Kumari ◽  
Obaid Alqahtani ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Linear Integral Equation ◽  
Dislocated Metric Space ◽  
Non Linear ◽  
Fractional Differential ◽  
Linear Integral ◽  
Dislocated Metric ◽  
Linear Fractional Differential Equations

In this article, we prove some fixed-point theorems in b-dislocated metric space. Thereafter, we propose a simple and efficient solution for a non-linear integral equation and non-linear fractional differential equations of Caputo type by using the technique of fixed point.

scholarly journals Coupled Fixed Point Theorems with New Implicit Relations and an Application

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
G. V. R. Babu ◽  
P. D. Sailaja
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Implicit Relation ◽  
Coupled Fixed Points

We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.

scholarly journals Cyclic generalized φ-contractions in b-metric spaces and an application to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2047-2057 ◽  
Author(s):  
Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Problem ◽  
Contractive Mappings

We introduce the notion of cyclic generalized ?-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented.

scholarly journals Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings

2015 ◽  
Vol 53 (1) ◽  
pp. 151-161
Author(s):  
Micah Okwuchukwu Osilike ◽  
Anthony Chibuike Onah
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iteration Scheme ◽  
Iteration Algorithm ◽  
Mann Iteration ◽  
Ishikawa Iteration ◽  
New Class ◽  
Hemicontractive Mappings ◽  
Demicontractive Mappings

Abstract A new class of α-hemicontractive maps T for which the strong convergence of the Ishikawa iteration algorithm to a fixed point of T is assured is introduced and studied. The study is a continuation of a recent study of a new class of α-demicontractive mappings T by L. Mărușter and Ș. Mărușter, Mathematical and Computer Modeling 54 (2011) 2486-2492 in which they proved strong convergence of the Mann iteration scheme to a fixed point of T. Our class of α-hemicontractive maps is more general than the class of α-demicontractive maps. No compactness assumption is imposed on the operator or it’s domain, and no additional requirement is imposed on the set of fixed points.

scholarly journals Fixed Points of Set-valued F-contraction Operators in Quasi-ordered Metric Spaces with an Application to Integral Equations

2021 ◽  
pp. 152-160
Author(s):  
Ehsan Lotfali Ghasab ◽  
Hamid Majani ◽  
Ghasem Soleimani Rad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Ordered Metric Spaces ◽  
Banach Contraction ◽  
Type Integral

In this paper, we prove some new fixed point theorems involving set-valued F-contractions in the setting of quasi-ordered metric spaces. Our results are significant since we present Banach contraction principle in a different manner from that which is known in the present literature. Some examples and an application to existence of solution of Volterra-type integral equation are given to support the obtained results

scholarly journals Common fixed point theorems under an implicit contractive condition on metric spaces endowed with an arbitrary binary relation and an application

2019 ◽  
pp. 2050146
Author(s):  
Md Ahmadullah ◽  
Mohammad Imdad ◽  
Mohammad Arif
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence Theorem ◽  
Binary Relation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Common Fixed Point Theorems

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well-known contraction conditions in one go besides yielding several new ones. We also provide an example to demonstrate the generality of our results over several well-known corresponding results of the existing literature. Finally, we utilize our results to prove an existence theorem for ensuring the solution of an integral equation.

scholarly journals On some fixed point theorems for multivalued F-contractions in partial metric spaces

2021 ◽  
Vol 54 (1) ◽  
pp. 151-161
Author(s):  
Santosh Kumar ◽  
Sholastica Luambano
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Partial Metric Spaces

Abstract Altun et al. explored the existence of fixed points for multivalued F F -contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F F -contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.

scholarly journals Existence of solution of Urysohn integral equation through generalized contractive mapping

2018 ◽  
Vol 38 (2) ◽  
pp. 101-113
Author(s):  
Om Prakash Chauhan ◽  
Deepak Singh ◽  
Vishal Joshi ◽  
Mahendra Singh Rathore
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Operator Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Existence Of Solution ◽  
Partially Ordered ◽  
The Given ◽  
Complex Valued

In this note, we establish the existence of fixed point through fixed point theorems in the setting of partially ordered complex valued b- metric spaces. Then this fixed point is co-related as solution of  equivalent operator equation of the Urysohn integral equation. In this process to make our results more authentic and meaningful we adopt an innovative way through visualling the given example supporting our findings. Naturally our results generalize some existing results.

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