Generalized Contractions to Coupled Fixed Point Theorems in Partially Ordered Metric Spaces

Rao, N. Seshagiri; Kalyani, K.

doi:10.17516/1997-1397-2020-13-4-492-502

Cited by 15 publications

(5 citation statements)

References 27 publications

(31 reference statements)

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“…Following that, Lakshmikantham and Ćirić [ 22 ], which were the extensions of [ 11 ] involving monotone property to a function in the space, pioneered the idea of coupled coincidence, common fixed point results. [ 19 , 25 , 34 – 37 ] provide additional information on coupled fixed point effects in various spaces under various contractive conditions.…”

Section: Introductionmentioning

confidence: 99%

Fixed point results for weak contractions in partially ordered b-metric space

2021

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Objectives We explore the existence of a fixed point as well as the uniqueness of a mapping in an ordered b-metric space using a generalized $$({\check{\psi }}, \hat{\eta })$$ ( ψ ˇ , η ^ ) -weak contraction. In addition, some results are posed on a coincidence point and a coupled coincidence point of two mappings under the same contraction condition. These findings generalize and build on a few recent studies in the literature. At the end, we provided some examples to back up our findings. Result In partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and also investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.

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Section: Introductionmentioning

confidence: 99%

Fixed point results for weak contractions in partially ordered b-metric space

2021

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“…Numerous publications [20][21][22] investigated fixed point results of various forms, including single, coupled, tripled, and others. Using the mixed monotone property, Bhaskar, Lakshmikantham [15], in 2006, proved some results of coupled fixed point.…”

Section: Application To Coupled Point Theorymentioning

confidence: 99%

Application to fixed point theory of α-θ-E-Geraghty Pata proximal contractions

Alam

Rohen

Albargi

et al. 2023

Preprint

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Here, we discuss the idea of α-θ-E-Geraghty Pata proximal contraction and weak ϕ-α-θ-E-Geraghty Pata proximal contraction by merging contraction criteria put forth by Pata and Geraghty utilizing the α-θ-proximal admissibility. In both standard as well as partially ordered metric spaces, for such proximal contractions, we present proximity point results for both single as well as multivalued mappings. We also investigate the existence of coupled fixed point for α-θ-E-Geraghty Pata type contractions in regular metric space. Numerous findings in the literature are generalized, expanded upon, and unified by these findings. We provide an application of fractional differential and few examples to demonstrate how outstanding our findings are. MSC Classification: 46T99 , 54E50 , 47H10 , 54H10

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“…[ 29 , 30 ] An operator , where is a non-empty set is said to be a b -metric, if it satisfies the properties given below (i) , (ii) , (iii) , for all and for some real number . Then is known as a b -metric space.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

Variations of generalized weak contractions in partially ordered b-metric space

Rao

Kalyani

2022

BMC Res Notes

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Objectives This paper explored the fixed point results for the mappings satisfying generalized weak contractive conditions in a complete partially ordered b-metric space. These contractions are some variations of the work done by the authors (Mituku et al. in BMC Res Notes 13:537. https://doi.org/10.1186/s13104-020-05354-1, 2020; Seshagiri et al. in BMC Res Notes 13:451. https://doi.org/10.1186/s13104-020-05273-1, 2020, BMC Res Notes 14:390. https://doi.org/10.1186/s13104-021-05801-7, 2021, BMC Res Notes 14:263. https://doi.org/10.1186/s13104-021-05649-x, 2021) in the same context. To validate the results a few examples are provided. Result The aim of this work is to prove some fixed point results of the self mappings in ordered b-metric space satisfying variant generalized weak contraction conditions. These results generalize some known results in the provided literature.

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Generalized Contractions to Coupled Fixed Point Theorems in Partially Ordered Metric Spaces

Cited by 15 publications

References 27 publications

Fixed point results for weak contractions in partially ordered b-metric space

Fixed point results for weak contractions in partially ordered b-metric space

Application to fixed point theory of α-θ-E-Geraghty Pata proximal contractions

Variations of generalized weak contractions in partially ordered b-metric space

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