Some Results on Fixed Points of Nonlinear Contraction in Metric Space

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽

10.3390/sym13030501 ◽

2021 ◽

Vol 13 (3) ◽

pp. 501

Author(s):

Ahmed Boudaoui ◽

Khadidja Mebarki ◽

Wasfi Shatanawi ◽

Kamaleldin Abodayeh

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fixed Points ◽

Metric Space ◽

Fixed Point Theorems ◽

Coupled Fixed Point ◽

Sufficient Conditions ◽

Impulsive Differential Equations ◽

System Of Differential Equations ◽

Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

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Fixed point theorems for expansive mappings in Gp-metric spaces

Creative Mathematics and Informatics ◽

10.37193/cmi.2017.03.07 ◽

2017 ◽

Vol 26 (3) ◽

pp. 297-308

Author(s):

MELTEM KAYA ◽

◽

HASAN FURKAN ◽

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Common Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Partial Metric ◽

Expansive Mapping ◽

Partial Metric Spaces ◽

Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

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The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

Canadian Mathematical Bulletin ◽

10.4153/cmb-2015-029-x ◽

2016 ◽

Vol 59 (01) ◽

pp. 3-12 ◽

Cited By ~ 2

Author(s):

Monther Rashed Alfuraidan

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Orlicz Spaces ◽

Multivalued Mappings ◽

Linear Spaces ◽

Modular Metric Spaces ◽

Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

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Common fixed points for multimaps in a metric space

Nonlinear Analysis ◽

10.1016/0362-546x(89)90051-5 ◽

1989 ◽

Vol 13 (3) ◽

pp. 221-229 ◽

Cited By ~ 6

Author(s):

K.P.R. Sastry ◽

S.V.R. Naidu ◽

J.R. Prasad

Keyword(s):

Fixed Points ◽

Metric Space ◽

Common Fixed Points

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Fuzzy fixed points of generalized F2-Geraghty type fuzzy mappings and complementary results

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2016.2.9 ◽

2016 ◽

Vol 21 (2) ◽

pp. 274-292 ◽

Cited By ~ 3

Author(s):

Mujahid Abbas ◽

Basit Ali ◽

Ornella Rizzo ◽

Calogero Vetro

Keyword(s):

Fixed Point ◽

Computer Science ◽

Fixed Points ◽

Metric Space ◽

Type Theorem ◽

Theoretical Computer Science ◽

Theoretical Computer ◽

Hybrid Pair ◽

Fuzzy Fixed Point

The aim of this paper is to introduce generalized F2-Geraghty type fuzzy mappings on a metric space for establishing the existence of fuzzy fixed points of such mappings. As an application of our result, we obtain the existence of common fuzzy fixed point for a generalized F2-Geraghty type fuzzy hybrid pair. These results unify, generalize and complement various known comparable results in the literature. An example and an application to theoretical computer science are presented to support the theory proved herein. Also, to suggest further research on fuzzy mappings, a Feng–Liu type theorem is proved.

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On Unique and Nonunique Fixed Points and Fixed Circles in M v b -Metric Space and Application to Cantilever Beam Problem

Journal of Function Spaces ◽

10.1155/2021/6681044 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Meena Joshi ◽

Anita Tomar ◽

Hossam A. Nabwey ◽

Reny George

Keyword(s):

Differential Equation ◽

Fixed Points ◽

Metric Space ◽

Order Differential Equation ◽

Unique Fixed Point ◽

Elastic Beam ◽

Closed Ball ◽

Open Ball ◽

Ball Convergence ◽

Fourth Order Differential Equation

We introduce M v b -metric to generalize and improve M v -metric and unify numerous existing distance notions. Further, we define topological notions like open ball, closed ball, convergence of a sequence, Cauchy sequence, and completeness of the space to discuss topology on M v b -metric space and to create an environment for the survival of a unique fixed point. Also, we introduce a notion of a fixed circle and a fixed disc to study the geometry of the set of nonunique fixed points of a discontinuous self-map and establish fixed circle and fixed disc theorems. Further, we verify all these results by illustrative examples to demonstrate the authenticity of the postulates. Towards the end, we solve a fourth order differential equation arising in the bending of an elastic beam.

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FIXED POINTS FOR TWO PAIRS OF ABSORBING MAPPINGS IN WEAK PARTIAL METRIC SPACES

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2002283p ◽

2020 ◽

pp. 283

Author(s):

Valeriu Popa ◽

Alina-Mihaela Patriciu

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Fixed Points ◽

Point Theorem ◽

Metric Space ◽

Metric Spaces ◽

Partial Metric Space ◽

Partial Metric ◽

Partial Metric Spaces

In this paper, a general fixed point theorem for two pairs of absorbing mappings in weak partial metric space, using implicit relations, has been proved.

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Convergence and Stability Results of Modified CUIA Iterative Scheme for Hyperbolic Convex Metric space

Journal of Physics Conference Series ◽

10.1088/1742-6596/2089/1/012040 ◽

2021 ◽

Vol 2089 (1) ◽

pp. 012040

Author(s):

Surjeet Singh Chauhan Gonder ◽

Khushboo Basra

Keyword(s):

Fixed Points ◽

Integral Equations ◽

Metric Space ◽

Iterative Scheme ◽

Real Life ◽

Convex Metric Space ◽

Convergence And Stability ◽

Life Problems ◽

Stability Results ◽

Differential And Integral Equations

Abstract The iterative fixed points have numerous applications in locating the solution of some real-life problems which can be modelled into linear as well as nonlinear differential and integral equations. In this manuscript, first of all, a new iterative scheme namely Modified CUIA iterative scheme is introduced. We first prove a theorem to check the convergence of this iteration for Hyperbolic Convex metric space. The result is then supported with one example. Further, another theorem is proved establishing the weak T stability of modified CUIA iterative scheme on the above space.

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Coupled fixed points of monotone mappings in a metric space with a graph

Fixed Point Theory ◽

10.24193/fpt-ro.2018.1.04 ◽

2018 ◽

Vol 19 (1) ◽

pp. 33-44

Author(s):

Monther Rashed Alfuraidan ◽

◽

Mohamed Amine Khamsi ◽

Keyword(s):

Fixed Points ◽

Metric Space ◽

Monotone Mappings ◽

Coupled Fixed Points

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