Article Review: Survey about Generalizing Distances

Authors

  • Shaimaa S. Al-Bundi Department of mathematics, College of Education for Pure science Ibn Haitham, university of Baghdad

DOI:

https://doi.org/10.24297/jam.v21i.9170

Keywords:

Generalizing Distances, set theory, descriptive set theory, measure theory, functional analysis, metric space

Abstract

As known, in general topology the talking be about “nearness”. This is exactly needed to discuss subjects such convergence and continuity. The simple way to study about nearness is to correspond the set with a distance function to inform us how far apart two elements of are. The metric concept introduced by a French mathematician Maurice René Fréchet (1878 – 1973) in 1906 in his work on some points of the functional calculus. However, the name is due to a German mathematician Felix Hausdorff (1868 –1942) who is considered to be one of the founders of modern topology. In addition to these contribution, he contributed significantly to set theory, descriptive set theory, measure theory, and functional analysis.

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References

G. L. Cain, “Introduction to General Topology 1st Edition”, Pearson, 1st edition, 2001.

R. Singh, J. Aggarwal “Introduction to metric space”, Institute of Lifelong Learning University of Delhi, 2016.

https://stats.stackexchange.com/questions/99171/why-is-euclidean-distance-not-a-good-metric-in-high-dimensions.

https://en.wikipedia.org/wiki/Metric_(mathematics)

M. Ayyash , “A Framework for a Minkowski Distance Based Multi Metric Quality of Service Monitoring Infrastructure for Mobile Ad Hoc Networks”, Inter. J. onElec. Engi. and Info., Vol. 4, No. 2, 2012.

J. Valente de Oliveira,W. Pedrycz, Advances in Fuzzy Clustering and its Applications, John Wiley & Sons, Ltd, 2007.

H. Xu; W. Zeng; X. Zeng; G. G. Yen, “An Evolutionary Algorithm Based on Minkowski Distance for Many-Objective Optimization”, IEEE Transactions on Cybernetics, Vol. 49, Issue:11, 2019.

I. Beg, A. R. Butt, “Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces”, Nonlinear Anal.,71, pp.3699-3704, 2009.

J. R. Giles, J R. Giles, “Introduction to the Analysis of Metric Spaces”, Cambridge University Press, 1987.

N. Shahzada, M. A. Alghamdia , S. Alshehrib , I. Aranđelovićc., “Semi-metric spaces and fixed points of α-ϕ-contractive maps”, J. Nonlinear Sci. Appl. 9, 3147–3156, 2016.

S. Czerwik, “Contraction mappings in b-metric spaces”. Acta Math. Inform. Univ. Ostrav. 1, pp. 5-11,1993.

I. A. Bakhtin, “The contraction principle in quasi-metric spaces”, Funct. Anal., 30, pp. 26-37, 1989.

S. K. Mohanta, “Some fixed point theorems using wt-distance in b-metric spaces”, Fasciculi Math., pp. 54125-140, 2015.

C. Sanjay, “A Simplified Book on Metric Spaces: The Right Way of Learning Metric Spaces”, LAP LAMBERT Academic Publishing, 2021

Z. Mustafa, H. Aydi, H. Karapinar, “On common fixed points in G-metric spaces using(E.A)property”, 64, pp. 1944-1956, 2012.

I. M. Erhan, E. Karapinar, T. Sekuli'c, “Fixed points of (φ,∅) contractions on rectangular metric spaces”, Fixed Point Theory Appl.,12, 2012.

A. Aghajani, M. Abbas, J. Roshan, “Common fixed point of generalized weak contraction mappings in partially ordered b-metric spaces”, Math. Slovaca, in press.

A. Amini-Harandi, “Fixed point theory for quasi-contraction maps in b-metric spaces”, Fixed Point Theory, 15, pp. 351-358, 2014.

I. A. Bakhtin, “The contraction principle in quasi-metric spaces”, Funct. Anal 30, 26-37., 1989.

N. Hussain, D. Dori'c, Z. Kadelburg, S. Radenovi'c, “Suzuki-type fixed point results in metric type spaces”, Fixed Point Theory Appl., 12pages, 2012.

N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, “Fixed points of cyclic weakly (φ,∅, L, A,B)-contractive mappings in ordered b-metric spaces with applications”, Fixed Point Theory Appl., 18 pages, 2013.

M. Jovanovi'c, Z. Kadelburg, S. Radenovi'c , “Common fixed point results in metric-type spaces”, Fixed Point Theory Appl.,15 pages 2010.

M. A. Khamsi, N. Hussain, “KKM mappings in metric type spaces”, Nonlinear Anal., 73, pp. 3123-3129, 2010.

M. Kir, H. Kiziltunc, “On Some Well Known Fixed Point Theorems in b-Metric Spaces”, Turkish Journal of Analysis and Number Theory, 1, pp. 13-16, 2013.

N. V. Dung, “Remarks on quasi-metric spaces”, Miskolc Mathematical Notes, 15(2) pp. 401-422, 2014.

J. R. Roshan, N. Hussain, V. Parvaneh, Z. Kadelburg, "New fixed point results in rectangular b-metric spaces”, 21, pp. 614-634, 2016.

B. Samet, W. Shatanawi, M. Abbas, “Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces”, pp. 680-687, 2012.

M. Boriceanu, “Fixed point theory for multivalued generalized contraction on a set with two b-metrics” ,Studia Univ. Babes Bolyai, Mathematica, Liv, No. 3, 2009.

T. Kamran, M. Samreen, , Q. UL Ain, “A generalization of b-metric space and some fixed point theorems”. Mathematics, 5(2), 19, 2017.

M. J. Mousa, S. S. Abed, “Coincidence points in

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Published

2022-02-08

How to Cite

Al-Bundi, S. S. . (2022). Article Review: Survey about Generalizing Distances. JOURNAL OF ADVANCES IN MATHEMATICS, 21, 5–14. https://doi.org/10.24297/jam.v21i.9170

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