scholarly journals A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1575
Author(s):  
Valentín Gregori ◽  
Juan-José Miñana ◽  
David Miravet
Keyword(s):  
Partial Metric ◽  
Classical Duality ◽  
Partial Metrics

In 1994, Matthews introduced the notion of partial metric and established a duality relationship between partial metrics and quasi-metrics defined on a set X. In this paper, we adapt such a relationship to the fuzzy context, in the sense of George and Veeramani, by establishing a duality relationship between fuzzy quasi-metrics and fuzzy partial metrics on a set X, defined using the residuum operator of a continuous t-norm ∗. Concretely, we provide a method to construct a fuzzy quasi-metric from a fuzzy partial one. Subsequently, we introduce the notion of fuzzy weighted quasi-metric and obtain a way to construct a fuzzy partial metric from a fuzzy weighted quasi-metric. Such constructions are restricted to the case in which the continuous t-norm ∗ is Archimedean and we show that such a restriction cannot be deleted. Moreover, in both cases, the topology is preserved, i.e., the topology of the fuzzy quasi-metric obtained coincides with the topology of the fuzzy partial metric from which it is constructed and vice versa. Besides, different examples to illustrate the exposed theory are provided, which, in addition, show the consistence of our constructions comparing it with the classical duality relationship.

scholarly journals On partial metric preserving functions and their characterization

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2315-2327
Author(s):  
Juan-José Miñana ◽  
Oscar Valero
Keyword(s):  
Functional Equation ◽  
Partial Metric ◽  
Generalized Metric ◽  
Metric Functions ◽  
Partial Metrics ◽  
The Relationship

In 1981, J. Bors?k and J. Dob?s characterized those functions that allow to transform a metric into another one in such a way that the topology of the metric to be transformed is preserved. Later on, in 1994, S.G. Matthews introduced a new generalized metric notion known as partial metric. In this paper, motivated in part by the applications of partial metrics, we characterize partial metric-preserving functions, i.e., those functions that help to transform a partial metric into another one. In particular we prove that partial metric-preserving functions are exactly those that are strictly monotone and concave. Moreover, we prove that the partial metric-preserving functions preserving the topology of the transformed partial metric are exactly those that are continuous. Furthermore, we give a characterization of those partial-metric preserving functions which preserve completeness and contractivity. Concretely, we prove that completeness is preserved by those partial metric-preserving functions that are non-bounded, and contractivity is kept by those partial metric-functions that satisfy a distinguished functional equation involving contractive constants. The relationship between metric-preserving and partial metric-preserving functions is also discussed. Finally, appropriate examples are introduced in order to illustrate the exposed theory.

The Coping Scales From the German Stress and Coping Questionnaire for Children and Adolescents

2020 ◽  
Vol 36 (4) ◽  
pp. 545-553 ◽  
Author(s):  
Heike Eschenbeck ◽  
Uwe Heim-Dreger ◽  
Denise Kerkhoff ◽  
Carl-Walter Kohlmann ◽  
Arnold Lohaus ◽  
...  
Keyword(s):  
Emotion Regulation ◽  
Children And Adolescents ◽  
Internal Consistency ◽  
Stress And Coping ◽  
Self Report ◽  
Partial Metric ◽  
Confirmatory Factor Analyses ◽  
Language Version ◽  
English Speaking ◽  
And Coping

Abstract. The coping scales from the Stress and Coping Questionnaire for Children and Adolescents (SSKJ 3–8; Lohaus, Eschenbeck, Kohlmann, & Klein-Heßling, 2018 ) are subscales of a theoretically based and empirically validated self-report instrument for assessing, originally in the German language, the five strategies of seeking social support, problem solving, avoidant coping, palliative emotion regulation, and anger-related emotion regulation. The present study examined factorial structure, measurement invariance, and internal consistency across five different language versions: English, French, Russian, Spanish, and Ukrainian. The original German version was compared to each language version separately. Participants were 5,271 children and adolescents recruited from primary and secondary schools from Germany ( n = 3,177), France ( n = 329), Russia ( n = 378), the Dominican Republic ( n = 243), Ukraine ( n = 437), and several English-speaking countries such as Australia, Great Britain, Ireland, and the USA (English-speaking sample: n = 707). For the five different language versions of the SSKJ 3–8 coping questionnaire, confirmatory factor analyses showed configural as well as metric and partial scalar invariance (French) or partial metric invariance (English, Russian, Spanish, Ukrainian). Internal consistency coefficients of the coping scales were also acceptable to good. Significance of the results was discussed with special emphasis on cross-cultural research on individual differences in coping.

Conceptualizing Protective Family Context and Its effect on Substance Use: Comparisons Across Diverse Ethnic-Racial Youth

2019 ◽  
Author(s):  
Kevin Constante ◽  
Edward Huntley ◽  
Emma Schillinger ◽  
Christine Wagner ◽  
Daniel Keating
Keyword(s):  
Substance Use ◽  
Measurement Invariance ◽  
Latent Variables ◽  
Latent Variable ◽  
Path Model ◽  
Family Context ◽  
Partial Metric ◽  
Racial Groups ◽  
Protective Methods ◽  
Family Variables

Background: Although family behaviors are known to be important for buffering youth against substance use, research in this area often evaluates a particular type of family interaction and how it shapes adolescents’ behaviors, when it is likely that youth experience the co-occurrence of multiple types of family behaviors that may be protective. Methods: The current study (N = 1716, 10th and 12th graders, 55% female) examined associations between protective family context, a latent variable comprised of five different measures of family behaviors, and past 12 months substance use: alcohol, cigarettes, marijuana, and e-cigarettes. Results: A multi-group measurement invariance assessment supported protective family context as a coherent latent construct with partial (metric) measurement invariance among Black, Latinx, and White youth. A multi-group path model indicated that protective family context was significantly associated with less substance use for all youth, but of varying magnitudes across ethnic-racial groups. Conclusion: These results emphasize the importance of evaluating psychometric properties of family-relevant latent variables on the basis of group membership in order to draw appropriate inferences on how such family variables relate to substance use among diverse samples.

scholarly journals Brief parental self-efficacy scales for promoting healthy eating and physical activity in children: a validation study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Åsa Norman ◽  
Julie Wright ◽  
Emma Patterson
Keyword(s):  
Physical Activity ◽  
Construct Validity ◽  
Sex Education ◽  
Self Efficacy ◽  
Parental Education ◽  
Weight Status ◽  
Preliminary Evidence ◽  
Objective Measures ◽  
Partial Metric ◽  
Invariance Testing

Abstract Background Brief scales to measure parental self-efficacy (PSE) in relation to children’s obesogenic behaviours have not been developed and validated using more rigorous methodology such as invariance testing, limiting their generalisability to sub-groups. This study aimed to assess the construct validity and measurement invariance of brief PSE scales for children’s intake of vegetables, soft drinks, and sweets, and physical activity. Methods Parents (n = 242) of five-to-seven-year-old children in disadvantaged and culturally diverse settings in Sweden responded to a questionnaire in Swedish with 12 items assessing PSE in relation to healthy and unhealthy behaviours. Construct validity was assessed with confirmatory factor analysis, invariance testing compared the scales by groups of parental sex, education, and child weight status. Criterion validity was evaluated using objective measures of children’s physical activity and semi-objective measures of diet. Results Two-factor models showed moderate to excellent fit to the data. Invariance was supported across all groups for healthy behaviour scales. Unhealthy behaviour scales were invariant for all groups except parental education where partial metric invariance was supported. Scales were significantly correlated with physical activity and diet. Conclusion This study provides preliminary evidence for the validity of brief PSE scales and invariance across groups suggesting their utility for research and clinical management of weight-related behaviours.

scholarly journals Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dušan Ðukić ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces ◽  
Type Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

Fixed point theorems for expansive mappings in Gp-metric spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 297-308
Author(s):  
MELTEM KAYA ◽  
◽  
HASAN FURKAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Expansive Mapping ◽  
Partial Metric Spaces ◽  
Weak Compatibility

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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