Characterizing weak compatibility in terms of weighted quartets

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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Co-delivery of Simvastatin and Demineralized Bone Matrix Hierarchically from Nanosheet-based Supramolecular Hydrogels for Osteogenesis

Journal of Materials Chemistry B ◽

10.1039/d1tb01256h ◽

2021 ◽

Author(s):

Xiao Zhang ◽

Jiabing Fan ◽

Chen Chen ◽

Tara Aghaloo ◽

Min Lee

Keyword(s):

Tissue Engineering ◽

Demineralized Bone Matrix ◽

Bone Matrix ◽

Therapeutic Agents ◽

Engineering Applications ◽

3D Scaffolds ◽

Hydrogel Scaffolds ◽

Delivery Platform ◽

Weak Compatibility ◽

Demineralized Bone

Supramolecular hydrogels are widely used as 3D scaffolds and delivery platform in tissue engineering applications. However, hydrophobic therapeutic agents exhibit weak compatibility in hydrogel scaffolds along with aggregation and precipitate....

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Feasibility Study of Chemical Treatments on Sorghum Fibres for Compatibility Enhancement in Polypropylene Composites

Materials Science Forum ◽

10.4028/www.scientific.net/msf.929.70 ◽

2018 ◽

Vol 929 ◽

pp. 70-77 ◽

Cited By ~ 1

Author(s):

Ismojo ◽

Rai Pratama ◽

Ghiska Ramahdita ◽

Anne Zulfia Syahrial ◽

Mochamad Chalid

Keyword(s):

Crystallinity Index ◽

Ester Group ◽

Hydroxyl Group ◽

Compatibility Study ◽

Scanning Calorimetry ◽

Polypropylene Composites ◽

Dsc Measurements ◽

Long Time ◽

Weak Compatibility ◽

Pp Composites

Polypropylene (PP) is one of the biggest petro-polymers, which is used in very wide application nowadays. The environment problem due to materials such as plastics having very long time degradability, and critical petroleum sources have promoted some studies to empowerment of natural resources such as natural fibres for substituting or at least modifying petro-polymers. Because of biodegradability obtained from natural source, sorghum fibers are interesting to be used as filler in PP composites, despite of weak compatibility between them. Surface modification on the sorghum fibers through alkalinization prior to acetylation was aimed to improve the fiber compatibility to PP. The treatments were expected to substitute hydroxyl group in the sorghum fibers, into acetic ester group in order to increase their hydrophobicity as the fillers. Moreover, the treatments were able to unbundle single fibers into micro-fibrillated cellulose (MFC) fibres with increase in crystallinity index. Usage of this MFC fiber as filler in PP leads to improvement of the composite performances such as thermal properties. In this study, Fourier Transformation Infra-Red (FTIR) Spectroscopy, X-ray Diffraction (XRD), Differential Scanning Calorimetry (DSC) and Field-Emission Scanning Electron Microscope (FE-SEM) were used to evaluate the performances of the Sorghum fibers after the treatments and as the filler in the Sorghum fibers/PP composites. The experimental results showed the MFC fibers as the smallest sizes in 5.0 microns and the highest crystallinity index up to 79.1 %, obtained from alkalinization with 2.5 M NaOH prior to acetylation with 17.4 M CH3COOH and the glacial (CH3CO2)2. Compatibility study of the treated Sorghum fibers on PP shows an improvement indicated by a strong interaction between the fibers and PP on morphology observation, increase in melting point of PP from 163.4°C (using virgin Shorgum fibers) into 163.6°C (using treated Sorghum fibers) in DSC measurements.

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Common fixed point theorems under contractive conditions of integral type in symmetric spaces

Demonstratio Mathematica ◽

10.1515/dema-2013-0489 ◽

2013 ◽

Vol 46 (4) ◽

Author(s):

F. Merghadi ◽

C. Godet-Thobie

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Symmetric Spaces ◽

Fixed Point Theorems ◽

Integral Type ◽

Weak Compatibility ◽

Common Fixed Point Theorems

AbstractThe purpose of this paper is to prove common fixed point theorems for a family of mappings in symmetric spaces using the property (E.A) and weak compatibility or occasionally weak compatibility. Our results extend some recent results.

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Fixed Point Theorem in Fuzzy Metric Space Through Weak Compatibility

Journal of Analysis & Number Theory ◽

10.18576/jant/050101 ◽

2017 ◽

Vol 5 (1) ◽

pp. 1-4

Author(s):

Amit Kumar Govery ◽

Mamta Singh

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Metric Space ◽

Fuzzy Metric Space ◽

Fuzzy Metric ◽

Weak Compatibility

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A common fixed point theorem using implicit relation and property (E.A) in metric spaces

Filomat ◽

10.2298/fil0702211p ◽

2007 ◽

Vol 21 (2) ◽

pp. 211-234 ◽

Cited By ~ 21

Author(s):

H. Pathak ◽

Rosana Rodriguez-López ◽

R.K. Verma

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Common Fixed Point ◽

Point Theorem ◽

Metric Spaces ◽

Contractive Condition ◽

Implicit Relation ◽

Weak Compatibility ◽

Common Fixed Point Theorem

In this paper, we prove a common fixed point theorem for a quadruple of mappings by using an implicit relation [6] and property (E.A) [1] under weak compatibility. Our theorem improves and generalizes the main Theorems of Popa [6] and Aamri and Moutawakil [1] .Various examples verify the importance of weak compatibility and property (E.A) in the existence of common fixed point and examples are also given to the implicit relation and to validate our main Theorem. We also show that property (E.A) and Meir-Keeler type contractive condition are independent to each other. .

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Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space

Journal of Mathematics ◽

10.1155/2020/1712486 ◽

2020 ◽

Vol 2020 ◽

pp. 1-16

Author(s):

Mi Zhou ◽

Xiao-lan Liu ◽

Nicolae Adrian Secelean

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Fuzzy Metric Space ◽

Fuzzy Metric Spaces ◽

Fuzzy Metric ◽

Weak Compatibility ◽

New Type ◽

Common Fixed Point Theorems

In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature.

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