<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>ψ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Meir-Keeler Contraction Mappings in Generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:math>-Metric Spaces

Karapınar, Erdal; Czerwik, Stefan; Aydi, Hassen

doi:10.1155/2018/3264620

Cited by 74 publications

(57 citation statements)

References 13 publications

(13 reference statements)

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“…By merging Equations (20) and (22), we deduce that σ(x * , Tx * ) = σ(Sx * , x * ). In addition, by Equations (21) and (23), we deduce that σ(Sx…”

Section: Resultsmentioning

confidence: 99%

“…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%

See 1 more Smart Citation

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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“…By merging Equations (20) and (22), we deduce that σ(x * , Tx * ) = σ(Sx * , x * ). In addition, by Equations (21) and (23), we deduce that σ(Sx…”

Section: Resultsmentioning

confidence: 99%

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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show abstract

“…For further attractive results, more examples with details see e.g. [2,4]- [9]- [10]- [13], [17], [22], [18], [19], [36], [23], [24] and the references therein.…”

Section: Theorem 11 ([28]mentioning

confidence: 99%

Interpolative Rus-Reich-Ćirić Type Contractions via Simulation Functions

Karapınar

Agarwal

2019

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…In 1993, S. Czerwik [1] extensively used the concept of b-metric space by replacing triangular inequality with a relatively more general condition which is also utilized to extend Banach contraction theorem. By now there already exists considerable literature in b-metric spaces and for the work of this kind one can consult to [2][3][4][5][6][7][8] and similar others. In 2017, Kamran et al [9] introduced a new type of generalized b-metric space and termed it as extended b-metric space.…”

Section: Introductionmentioning

confidence: 99%

Extended Rectangular Mrξ-Metric Spaces and Fixed Point Results

et al. 2019

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In this paper, we enlarge the classes of rectangular M b -metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular M rξ -metric spaces and utilize the same to prove an analogue of Banach contraction principle in such spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of solution for a system of Fredholm integral equation. Mathematics 2019, 7, 1136 2 of 15 class extended M b -metric spaces. Very recently, Asim et al. [18] introduced the class of rectangular M b -metric space and utilized the same to prove an analogue of Banach contraction principle. Soon, Asim et al. [19] generalized the class of rectangular M b -metric spaces by introducing the class of M ν -metric spaces.Inspired by foregoing observations, we introduce the class of extended rectangular M rξ -metric spaces and utilize the same to prove fixed point result in such spaces. We, also furnish an example to establish the genuineness of our newly proved result. Finally, we use our main result to examine the existence and uniqueness of solution for a Fredholm integral equation. Definition 6.[12] Let χ = ∅ and ξ : χ × χ → [1, ∞). A mapping r ξ : χ × χ → R + is said to be an extended rectangular b-metric on χ if, r ξ satisfies the following (for all ς, σ ∈ χ and all distinct ρ, ∈ χ \ {ς, σ}):

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(α,ψ)-Meir-Keeler Contraction Mappings in Generalized b-Metric Spaces

Abstract: We present a fixed point theorem for generalized (α,ψ)-Meir-Keeler type contractions in the setting of generalized b-metric spaces. The presented results improve, generalize, and unify many existing famous results in the corresponding literature.

Cited by 74 publications

References 13 publications

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

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

Interpolative Rus-Reich-Ćirić Type Contractions via Simulation Functions

Extended Rectangular Mrξ-Metric Spaces and Fixed Point Results

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