scholarly journals Fixed Point Results for an Almost Generalized α -Admissible Z -Contraction in the Setting of Partially Ordered b-Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Solomon Gebregiorgis Teweldemedhin ◽  
Kidane Koyas Tola
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Simulation Function ◽  
Existence Of A Solution ◽  
Partially Ordered

In this paper, we introduce an almost generalized α -admissible Z -contraction with the help of a simulation function and study fixed point results in the setting of partially ordered b-metric spaces. The presented results generalize and unify several related fixed point results in the existing literature. Finally, we verify our results by using two examples. Moreover, one of our fixed point results is applied to guarantee the existence of a 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.

scholarly journals Kannan-Type Contractions on New Extended b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hassen Aydi ◽  
Muhammad Aslam ◽  
Dur-e-Shehwar Sagheer ◽  
Samina Batul ◽  
Rashid Ali ◽  
...  
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Asymptotic Regularity ◽  
Existence Of A Solution ◽  
Fredholm Type ◽  
Type Integral

This article is focused on the generalization of some fixed point theorems with Kannan-type contractions in the setting of new extended b -metric spaces. An idea of asymptotic regularity has been incorporated to achieve the new results. As an application, the existence of a solution of the Fredholm-type integral equation is presented.

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

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.

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

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