Fixed point theorems for generalized weakly contractive mappings in metric spaces with applications

Cho, Seonghoon

doi:10.1186/s13663-018-0628-1

Cited by 22 publications

(38 citation statements)

References 36 publications

(33 reference statements)

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“…We have already noted that the main result is an actual generalization of a previous result in [4]. The methodology here is comparable with several other similar results dealing with contractive inequalities noted in [3][4][5][6][7][8][9][10]. There are possibilities of applying relation-theoretic methods to other weakly contractive mappings.…”

Section: Discussionsupporting

confidence: 84%

“…In both cases, the aim is to retain the fixed point property of the relevant function under relaxed conditions. Some instances of works in the former line are [3][4][5][9][10][11] while references [23][24][25][26] are some works obtained in the latter line of research. Particularly, the present work directly extends the result of [4].…”

Section: Remarkmentioning

confidence: 99%

“…Afterwards, the idea was generalized and extended in several ways by which a large amount of literature on the fixed point theory of weakly contractive mappings was produced. Some instance of these works are [3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

2019

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In recent times there have been two prominent trends in metric fixed point theory. One is the use of weak contractive inequalities and the other is the use of binary relations. Combining the two trends, in this paper we establish a relation-theoretic fixed point result for a mapping which is defined on a metric space with an arbitrary binary relation and satisfies a weak contractive inequality for any pair of points whenever the pair of points is related by a given relation. The uniqueness is obtained by assuming some extra conditions. The metric space is assumed to be R-complete. We use R-continuity of functions. The property of local T-transitivity of the relation R is used in the main theorem. There is an illustrative example. An existing fixed point result is generalized through the present work. We use a method in the proof of our main theorem which is a blending of relation-theoretic and analytic approaches.

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Section: Discussionsupporting

confidence: 84%

Section: Remarkmentioning

confidence: 99%

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Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

2019

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“…It is widely used in many fields of mathematics. Due to its importance, many authors have generalized this result in various directions [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Ciric [1] introduced the concept of generalized contractions.…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Theorem for Cyclic Weakly Generalized Contraction Mapping of Ciric Type

Goyal¹,

Garg²

2020

J. Sci. Res.

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In this article, the concept of cyclic weakly generalized contraction mapping of Ciric type has been introduced and the existence of a fixed point for such mappings in the setup of complete metric spaces has been established. Result obtained extends and improves some fixed point results in the literature. Example is also given to show that class of contraction mappings introduced in the paper is strictly larger class than the class of mappings used in the literature and thus ensures wider applicability of the result by producing the solutions to new problems.

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“…This interesting subject has been mediated by certain authors, for example, see References [6][7][8]. In partial metric spaces and partially ordered metric-like spaces, the usual contractive condition is weakened and many researchers apply their results to problems of existence and uniqueness of solutions for some boundary value problems of differential and Integral equations, for example, see References [9][10][11][12][13][14][15][16][17][18][19][20][21][22] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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

Qawaqneh

Noorani

Shatanawi

et al. 2018

Axioms

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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.

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Fixed point theorems for generalized weakly contractive mappings in metric spaces with applications

Cited by 22 publications

References 36 publications

Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Fixed Point Theorem for Cyclic Weakly Generalized Contraction Mapping of Ciric Type

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

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