scholarly journals Solving a nonlinear integral equation via orthogonal metric space

2021 ◽  
Vol 7 (1) ◽  
pp. 1198-1210
Author(s):  
Arul Joseph Gnanaprakasam ◽  
◽  
Gunaseelan Mani ◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Admissible Mapping

<abstract><p>We propose the concept of orthogonally triangular $ \alpha $-admissible mapping and demonstrate some fixed point theorems for self-mappings in orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by our results. An instance to help our outcome is presented. We also explore applications of our key results.</p></abstract>

scholarly journals Some α − ϕ -Fuzzy Cone Contraction Results with Integral Type Application

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Saif Ur Rehman ◽  
Shamoona Jabeen ◽  
Sami Ullah Khan ◽  
Mohammed M. M. Jaradat
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Integral Type ◽  
Contraction Mappings ◽  
Theoretical Results ◽  
Cone Metric

In this paper, we define α -admissible and α - ϕ -fuzzy cone contraction in fuzzy cone metric space to prove some fixed point theorems. Some related sequences with contraction mappings have been discussed. Ultimately, our theoretical results have been utilized to show the existence of the solution to a nonlinear integral equation. This application is also illustrative of how fuzzy metric spaces can be used in other integral type operators.

scholarly journals Common Fixed Point Theorems for Generalized Geraghty (α,ψ,ϕ)-Quasi Contraction Type Mapping in Partially Ordered Metric-Like Spaces

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 74 ◽  
Author(s):  
Haitham Qawaqneh ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Habes Alsamir
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partially Ordered ◽  
Type Mapping ◽  
Admissible Mapping ◽  
Contraction Type ◽  
Common Fixed Point Theorems

The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show the superiority of our results. The obtained results progress some well-known fixed (common fixed) point results in the literature. Our main results cannot be specifically attained from the corresponding metric space versions. This paper is scientifically novel because we take Geraghty contraction self-mapping in partially ordered metric-like spaces via α − admissible mapping. This opens the door to other possible fixed (common fixed) point results for non-self-mapping and in other generalizing metric spaces.

scholarly journals Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Contractive Mappings

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

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 Two Fixed Point Theorems Concerning F-Contraction in Complete Metric Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 58 ◽  
Author(s):  
Ovidiu Popescu ◽  
Gabriel Stan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
The Self ◽  
Complete Metric Spaces

In this paper, we generalize some results of Wardowski (Fixed Point Theory Appl. 2012:94, 2012), Cosentino and Vetro (Filomat 28:4, 2014), and Piri and Kumam (Fixed Point Theory Appl. 2014:210, 2014) theories by applying some weaker symmetrical conditions on the self map of a complete metric space and on the mapping F, concerning the contractions defined by Wardowski.

scholarly journals Fixed points results via simulation functions

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2343-2350 ◽  
Author(s):  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Simulation Function ◽  
Complete Metric Spaces ◽  
Admissible Mapping ◽  
Simulation Functions

In this paper, we present some fixed point results in the setting of a complete metric spaces by defining a new contractive condition via admissible mapping imbedded in simulation function. Our results generalize and unify several fixed point theorems in the literature.

scholarly journals Some fixed point theorems relating to the orbital continuity

2005 ◽  
Vol 36 (1) ◽  
pp. 73-80 ◽  
Author(s):  
C. V. R. Babu ◽  
M. V. R. Kameswari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Asymptotically Regular

In this paper, we prove a fixed point theorem for asymptotically regular mappings on a metric space using orbital continuity of the selfmap. As an application of this result, a fixed point theorem is established in $T$-orbitally complete metric spaces. Our results extend Mukherjee's theorem [4] to $T$-orbitally complete metric spaces, and generalize the theorems of Jotic [5] and Neu{s}i'{c} [6].

scholarly journals SOME FIXED POINT THEOREMS FOR GENERALIZED $\alpha$-GERAGHTY CONTRACTION TYPE MAPPINGS IN $B$-METRIC~SPACES AND SOME APPLICATIONS TO THE NONLINEAR INTEGRAL EQUATION

2017 ◽  
pp. 231
Author(s):  
Nguyen Trung Hieu ◽  
Le Thi Chac
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Spaces ◽  
Type Mapping ◽  
Contraction Type

The purpose of this paper is to introduce the notion of a generalized $\alpha$-Geraghty contraction type mapping in $b$-metric~spaces and state the existence and uniqueness of a fixed point for this mapping. These results are generalizations of certain the main results in [D.~\DJ uki\'{c}, Z.~Kadelburg, and S.~Radenovi\'{c}, \emph{Fixed points of Geraghty-type mappings in various generalized metric spaces}, Abstr. Appl. Anal. \textbf{2011} (2011), 13 pages] and [O.~Popescu, \emph{ Some new fixed point theorems for $\alpha$-Geraghty contraction type maps in metric spaces}, Fixed Point Theory Appl. \textbf{2014:190} (2014), 1 -- 12]. Some examples are given to illustrate the obtained results and to show that these results are proper extensions of the existing ones. Then we apply the obtained theorem to study the existence of solutions to the nonlinear integral equation.

scholarly journals Some Fixed Point Theorems for Almost (GF; δb)-Contractions and Application

2017 ◽  
Vol 58 (1) ◽  
pp. 123-143 ◽  
Author(s):  
H. K. Nashine ◽  
R. P. Agarwal ◽  
S. Shukla ◽  
A. Gupta
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces

AbstractWe propose a new notion of multi-valued almost (GF; δb)-contractions involving rational terms under δ-distance on b-metric spaces and give its relevance to fixed point results in orbitally complete b-metric spaces. An ordered version of our main result is also proved with some weaker contractive conditions. Some examples are given to show the usability of the results proved herein. Moreover, application of our result to the nonlinear integral equation is given.

scholarly journals Solving a Nonlinear Fredholm Integral Equation via an Orthogonal Metric

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Arul Joseph Gnanaprakasam ◽  
Gunaseelan Mani ◽  
Vahid Parvaneh ◽  
Hassen Aydi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fredholm Integral Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Nonlinear Fredholm Integral Equation

In this paper, we prove fixed point theorems using orthogonal triangular α -admissibility on orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by the obtained results. An instance to help our outcome is being presented.

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