On Fixed-Point Results of Generalized Contractions

Kanwal, Shazia; Hanif, Umair; Noorwali, Maha; Alam, Md. Ashraful

doi:10.1155/2022/9167716

Cited by 3 publications

(4 citation statements)

References 13 publications

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“…It follows that the sequence {a n } n∈N∪{0} is a Cauchy sequence in (S, d). Also, from (7) and using n → ∞ gives lim n→∞ d(a n , a n+1 ) = 0.…”

Section: Extended Integral -Contractionmentioning

confidence: 99%

“…Neetu [6], proved the fixed-point result of contractive functions in cone b-metric spaces without a normality condition. Kanwal et al [7], introduced a new type of contractive condition for contractive mappings to prove the fixed-point theorems in the settings of b-metric space. More articles related to this study are in [8][9][10][11][12][13][14][15] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exploring Integral ϝ-Contractions with Applications to Integral Equations and Fractional BVPs

Nisar,

Mehmood,

Azam

et al. 2023

Fractal Fract

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In this article, two types of contractive conditions are introduced, namely extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction. For the case of two mappings and their coincidence point theorems, a variant of (ϰ,Ω-Ϝ)-contraction has been introduced, which is called (ϰ,Γ1,2,Ω-Ϝ)-contraction. In the end, the applications of an extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction are given by providing an existence result in the solution of a fractional order multi-point boundary value problem involving the Riemann–Liouville fractional derivative. An interesting existence result for the solution of the nonlinear Fredholm integral equation of the second kind using the (ϰ,Γ1,2,Ω-Ϝ)-contraction has been proven. Herein, an example is established that explains how the Picard–Jungck sequence converges to the solution of the nonlinear integral equation. Examples are given for almost all the main results and some graphs are plotted where required.

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“…It follows that the sequence {a n } n∈N∪{0} is a Cauchy sequence in (S, d). Also, from (7) and using n → ∞ gives lim n→∞ d(a n , a n+1 ) = 0.…”

Section: Extended Integral -Contractionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploring Integral ϝ-Contractions with Applications to Integral Equations and Fractional BVPs

Nisar,

Mehmood,

Azam

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…The aforementioned spaces have seen a great deal of development. The aforementioned spaces have recently been the focus of investigation into fixed point and common fixed point results for single-valued as well as multi-valued mappings; for examples, see Ali et al (6) , Khan et al (7) , Kanwel et al (8)(9)(10) , Tassaddiq et al (11) , Karapinar et al (12,13) , Qawaqneh et al (14) , Shoaib et al (15) , and the references within it.…”

Section: Introductionmentioning

confidence: 99%

Fixed Point and Common Fixed Point Theorems for Single Valued and Multivalued Mappings in Partial b-Metric Spaces

Tiwari,

Dewangan

2024

IJST

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Objectives: To prove some fixed point theorems and common fixed point theorems by using partial b-metric spaces. Methods: Ciric type contraction for single-valued mapping is also used to prove fixed point theorem and Nadler's type Banach contraction is used to produce fixed point and common fixed point theorems. Findings: We have to find fixed point and common fixed point theorems for single valued mapping and a fixed point theorem for multivalued mapping. Novelty : We have to use a new type of space called partial bmetric space to prove all the theorems in this paper. No one has proven these theorems before in this space.

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“…Then a mapping d : In 2010, Khamsi and Hussain [16] used the notion of b-metric space under the name metric type space. More on b-metric spaces can be studied in [17,18,19,20,21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Fixed Points of \(\xi\) - (\(\alpha\), \(\beta\))- Contractive Mappings in b-Metric Spaces

Jain¹,

Kaur

Bhatia

2023

JAMCS

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In the paper [Some new observations on Geraghty and \(\acute{C}\)iri\(\acute{c}\) type results in b-metric spaces, Mathematics, 7, (2019), doi: 10.3390/math7070643] Mlaiki et al. introduced (\(\alpha\), \(\beta\))-type contraction in order to generalize the contraction mapping defined by Pant and Panicker. Also, in the paper [Some fixed point results in b- metric spaces and b-metric-like spaces with new contractive mappings, Axioms, 10(2), (2021), 15 pages, doi: 10.3390/axioms10020055] Jain and Kaur presented the concepts of \(\xi\) -contractive mappings. Now, the aim of the present article is to introduce \(\xi\) - (\(\alpha\), \(\beta\)) -contractive mappings in b-metric spaces by combining the concepts (\(\alpha\), \(\beta\))-type contraction and \(\xi\)-contractive mappings. Also, we establish some fixed point results for newly defined mappings. Our results generalize various theorems in literature. In support, we provide an example.

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On Fixed-Point Results of Generalized Contractions

Cited by 3 publications

References 13 publications

Exploring Integral ϝ-Contractions with Applications to Integral Equations and Fractional BVPs

Exploring Integral ϝ-Contractions with Applications to Integral Equations and Fractional BVPs

Fixed Point and Common Fixed Point Theorems for Single Valued and Multivalued Mappings in Partial b-Metric Spaces

Fixed Points of \(\xi\) - (\(\alpha\), \(\beta\))- Contractive Mappings in b-Metric Spaces

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