scholarly journals Fixed point theorems for Ćirić type mapping and application to integral equation

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Jeong Sheok Ume
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Type Mapping

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 of rational type contraction in b-metric spaces

2021 ◽  
Vol 7 (3) ◽  
pp. 350-363
Author(s):  
Merdaci Seddik ◽  
Hamaizia Taieb
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Type Mapping ◽  
Contractive Type ◽  
Common Fixed Point Theorems ◽  
Rational Type ◽  
Type Contraction

Abstract In this paper, we prove some common fixed point theorems satisfying contractive type mapping in the setting of b-metric spaces. The presented theorem is an extension the results of M. Sarwar and M. U. Rahman [23] as well as a generalization of many well-known results in the literature through the context of b-metric spaces. Also, we present a few examples to illustrate the validity of the results obtained in the paper. Finally, results are applied to find the solution for an integral equation.

scholarly journals TEOREMA TITIK TETAP UNTUK PEMETAAN KANNAN PADA RUANG METRIK MODULAR TERITLAK

1970 ◽  
Vol 11 (2) ◽  
pp. 11
Author(s):  
Lusi Harini
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Modular Metric Space ◽  
Type Mapping ◽  
Kannan Mapping ◽  
Finite Set

In this paper, we will discuss about fixed point theorems in generalized modular metric space for Kannan-  type mapping. The existence of the fixed point of this mapping is guaranteed by providing that the mapping domain is a -finite set and the Kannan-  mapping constant  satisfied  where K is a constant from the axiom of generalized modular metric space.

scholarly journals A New Version of Schauder and Petryshyn Type Fixed Point Theorems in S-Modular Function Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 15
Author(s):  
Maryam Ramezani ◽  
Hamid Baghani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Convex Sets ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Modular Space ◽  
Ordinate Axis ◽  
Modular Function Spaces

In this paper, using the conditions of Taleb-Hanebaly’s theorem in a modular space where the modular is s-convex and symmetric with respect to the ordinate axis, we prove a new generalized modular version of the Schauder and Petryshyn fixed point theorems for nonexpansive mappings in s-convex sets. Our results can be applied to a nonlinear integral equation in Musielak-Orlicz space L p where 0 < p ≤ 1 and 0 < s ≤ p .

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 GENERALIZATIONS OF KANNAN'S THEOREMS VIA ΣC-FUNCTION AND ITS APPLICATION

2019 ◽  
Vol 24 (4) ◽  
pp. 530-549
Author(s):  
Suprokash Hazra ◽  
Satish Shukla
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Simulation Function ◽  
R Functions

In this article, we go on to discuss various proper extensions of Kannan’s two different fixed point theorems, and introduce the new concept of σc-function, which is independent of the three notions of simulation function, manageable functions, and R-functions. These results are analogous to some well-known theorems, and extend several known results in this literature. An application of the new results to the integral equation is also provided.

scholarly journals Common fixed points under Lipschitz type condition

1970 ◽  
Vol 7 (1) ◽  
pp. 74-78
Author(s):  
Vyomesh Pant
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Key Words And Phrases ◽  
Type Condition ◽  
Type Mapping ◽  
Common Fixed Point Theorems ◽  
Weak Commutativity

The present paper is aimed at obtaining common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R- weak commutativity but without assuming the completeness of the space or continuity of the mappings involved. Mathematics Subject Classification: 54 H 25. Key Words and Phrases: Lipschitz type mapping pairs, nonexpansive conditions, noncompatible mappings, Pointwise R-weak commutativity, contractive conditions. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5424 KUSET 2011; 7(1): 74-78

scholarly journals Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 130
Author(s):  
Mohamed Amine Farid ◽  
Karim Chaira ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Weak Topology ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Nonlinear Operator ◽  
Banach Algebras ◽  
Measure Of Weak Noncompactness

In this paper, we prove some fixed point theorems for the nonlinear operator A · B + C in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the application of our results to a nonlinear integral equation in Banach algebra.

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 Random Fixed Point Theorems of Random Comparable Operators and an Application

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Jiandong Yin ◽  
Zhongdong Liu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Monotone Operators ◽  
Hammerstein Integral Equation ◽  
Random Fixed Point ◽  
Partially Ordered ◽  
Ordered Banach Spaces

We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. Finally, as an application, we consider the existence of the solution of a random Hammerstein integral equation.

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