ON Ψ-PROJECTIVE EXPANSION, QUASI PARTIAL METRICS AGGREGATION WITH AN APPLICATION

Vishal Gupta; Pooja Dhawan; Jatinderdeep Kaur

doi:10.11948/20190171

2020 Volume 10 Issue 3

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2020 > 10(3): 946-959

Next Article Previous Article

Vishal Gupta, Pooja Dhawan, Jatinderdeep Kaur. ON Ψ-PROJECTIVE EXPANSION, QUASI PARTIAL METRICS AGGREGATION WITH AN APPLICATION[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 946-959. doi: 10.11948/20190171

Citation:

Vishal Gupta, Pooja Dhawan, Jatinderdeep Kaur. ON Ψ-PROJECTIVE EXPANSION, QUASI PARTIAL METRICS AGGREGATION WITH AN APPLICATION[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 946-959. doi: 10.11948/20190171

ON Ψ-PROJECTIVE EXPANSION, QUASI PARTIAL METRICS AGGREGATION WITH AN APPLICATION

1.
Department of Mathematics, Maharishi Markandeshwar, Deemed to be University, Mullana-133207, Haryana, India
2.
School of Mathematics, Thapar Institute of Engineering and Technology, Patiala(Punjab)-147004, India

Corresponding author: Email address: vishal.gmn@gmail.com, vgupta@mmumullana.org (V. Gupta)

Abstract

Abstract

In the present article, the notion of expansion between quasi partial metric spaces through aggregation is defined. With the help of aggregation functions, the concept of projective $\Psi$-expansion is introduced and some fixed point results are obtained through this notion. Furthermore, sufficient conditions are provided to characterize aggregation function and to ensure the existence and uniqueness of fixed point. All the results presented in this paper are new and an application to asymptotic complexity analysis is also given after the results.
- Fixed point /
- quasi partial metric space /
- aggregation function /
- projective expansion
MSC: 47H10, 54H25

FullText(HTML)

References

[1]	M. A. Alghamdi, N. Shahzad and O. Valero, Fixed point theorems in generalized metric spaces with applications to computer science, Fixed Point Theory and Applications, 2013, 118, 1-20. Google Scholar
[2]	M. A. Alghamdi, N. Shahzad and O. Valero, Projective contractions, generalized metrics, and fixed points, Fixed Point Theory and Applications, 2015, 181, 1-13. Google Scholar
[3]	J. Borsik and J. Dobo$\check{s}$, On a product of metric spaces, Mathemaica Slovaca, 1981, 31, 193-205. Google Scholar
[4]	M. J. Campión, R.G. Catalán, E. Induráin, I. Lizasoain, A. R. Pujol and O.Valero, Geometrical aggregation of finite fuzzy sets, International Journal of Approximate Reasoning, 2018, 103, 248-266. doi: 10.1016/j.ijar.2018.10.005 CrossRef Google Scholar
[5]	P. Dhawan and J. Kaur, Fixed Points of Expansive Mappings in Quasi Partial Metric Spaces, International Journal of Advanced Research in Science and Engineering, 2016, 5, 145-151. Google Scholar
[6]	V. Gupta, R. Deep and A. K. Tripathi, Existence of coincidence point for weakly increasing mappings satisfies $\left(\psi, \phi\right)$-weakly contractive condition in partially ordered metric spaces, International Journal of Computing Science and Mathematics, 2016, 7(6), 495-508. $\left(\psi, \phi\right)$-weakly contractive condition in partially ordered metric spaces" target="_blank">Google Scholar
[7]	R. Heckmann, Approximation of metric spaces by partial metric spaces, Applied Categorical Structures, 1999, 7, 71-83. doi: 10.1023/A:1008684018933 CrossRef Google Scholar
[8]	E. Karapinar, Fixed point theorems on quasi-partial metric spaces, Mathematical and Computer Modelling, 2013, 57, 2442-2448. doi: 10.1016/j.mcm.2012.06.036 CrossRef Google Scholar
[9]	W. Kirk and N. Shahzad, Fixed point theory in distance spaces, Cham: Springer, 2014. Google Scholar
[10]	J. Martin, G. Mayor and O. Valero, Aggregation of asymmetric distances in Computer Science, Information Sciences, 2010, 180, 803-812. doi: 10.1016/j.ins.2009.06.020 CrossRef Google Scholar
[11]	S. Massanet and O. Valero, New results on metric aggregation, Proceedings of the 17th Spanish Conference on Fuzzy Technology and Fuzzy Logic(Estylf2012), 2012, 558-563. Google Scholar
[12]	S. G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences, 1994, 728, 183-197. doi: 10.1111/j.1749-6632.1994.tb44144.x CrossRef Google Scholar
[13]	S. G. Matthews, An extension treatment of lazy data flow deadlock, Theoretical Computer Science, 1995, 151, 195-205. doi: 10.1016/0304-3975(95)00051-W CrossRef Google Scholar
[14]	G. Mayor and O. Valero, Metric aggregation functions revisited, European Journal of Combinatorics, 2019, 80, 390-400. doi: 10.1016/j.ejc.2018.02.037 CrossRef Google Scholar
[15]	J. J. Minana, An overview on transformations on generalized metrics, Workshop on Applied Topological Structures, Valencia, 2017, 95-102. Google Scholar
[16]	S. Romaguera, P. Tirado and O. Valero, Complete partial metric spaces have partially metrizable computational models, Internation Journal of Computer Mathematics, 2012, 89, 284-290. doi: 10.1080/00207160.2011.559229 CrossRef Google Scholar
[17]	S. Romaguera and O. Valero, A quantitative computational model for complete partial metric spaces via formal balls, Mathematical Structures in Computer Science, 2009, 19, 541-563. doi: 10.1017/S0960129509007671 CrossRef Google Scholar
[18]	W. Shatanawi and K. Abodayeh, Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces, Mathematics, 2019, 7, 453. doi: 10.3390/math7050453 CrossRef Google Scholar
[19]	W. Shatanawi, M. Salmi, M. D. Noorani, H. Alsamir and A. Bataihah, Fixed and common fixed point theorems in partially ordered quasi-metric spaces, Journal of Mathematics and Computer Science, 2016, 16, 516-528. doi: 10.22436/jmcs.016.04.05 CrossRef Google Scholar
[20]	S. Wang, B. Li, Z. Gao and K. Iseki, Some fixed point theorems on expansion mappings, Mathematica Japonica, 1984, 29, 631-636. Google Scholar