Fixed Point Theorems for 𝜓 − 𝜑 −
𝜆 Contractions in 𝑆𝑏 − Metric Spaces

K.P.R. Sastry; K.K.M. Sarma; P. Krishna Kumari

doi:https://doi.org/10.14445/22315373/IJMTT-V56P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 1 | Year 2018 | Article Id. IJMTT-V56P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P505

Fixed Point Theorems for 𝜓 − 𝜑 − 𝜆 Contractions in 𝑆𝑏 − Metric Spaces

K.P.R. Sastry, K.K.M. Sarma, P. Krishna Kumari

Abstract

In this paper we introduce 𝜓 − 𝜑 − 𝜆 contraction in an 𝑆𝑏 − metric space and prove fixed point theorems for 𝜓 − 𝜑 − 𝜆 contraction in 𝑆𝑏 −metric spaces. We also obtain an application of our result. Further an example in support of our result is given. Our results improve those of G.N.V Kishore et al

Keywords

Sb− metric space, fixed point, ψ - φ contraction, ψ - φ - λ contraction

References

1. A.Aghajani, M.Abbas, JR.Roshan: Common fixed point of generalized weak contraction mappings in partially ordered G b - Metric Spaces, Filomat 28(6), 1087-1101 (2014).
2. AH.Ansari, O.Ege, S.Randenovic: Some fixed point Results on complex valued G b Metric Spaces RACSAM (2017) doi: 10.1007 / s 13398-017-0391- x.
3. B.D. Dhage: Generalized metric spaces, mappings with fixed point. Bull, calcutta math Soc-84[1992], 329-336[in article].
4. G.N.V.Kishore, K.P.R Rao, D.Panthi, B.Srinivas Rao, S.Satyanarayana: Some applications via fixed point results in partially ordered Sb-Metric Spaces. (2017) 2017:10 – DOI/10 – 1186 / S / 13663 – 017 – 0603-2.
5. K. Kumara swamy, T. Phaneendra: Fixed point theorem for two self maps in the G-metric space. Bulletin of Mathematics and Statastics Research. A peer reviewed International National journal – Vol . 4, S.I. 2016: ISSN: 2348 – 0580.
6. K.P.R Sastry, G. Appala Naidu, B. Ramu Naidu: Fixed point theorem for the T – contraction on a G-metric space and consequences. International journal of scientific and enjineering research , Vol. 8, issue, feb – 2017, ISSN - 2229- 5518.
7. K.P.R Sastry, K.K.M Sarma, P. Krishna Kumari, Sunitha Choudari: Fixed Point Theorems for -contractions in S-Metric Spaces and K.K.S Metric Spaces. International Journal of Mathematics and its applications, Volume 5, Issue 4-E(2017), 619-632 with ISSN: 2347-1557.
8. K. Prudhvi: Some fixed point results in S- metric spaces – Journal of Mathmatical Sciences and applications. Vol.4, no. 1, 2016, PP 1 -3, doi: 10, 12691 / JMSA -4-1-1- research article.
9. NT.Hein, NT.Thanhly, NV.Dury: A generalization of ciric quasi contraction for mapping on S-metric spaces Thas.J.Malt – 13369 – 380 [2014].
10. R. chugh, T.Kadian, A. Ram, B.C. Rhoades: Property P in G-metric spaces, Fixed point theory appl. Vol. 2010, Article ID 401684.
11. S.Czerwik:. Contraction mapping in b-Metric Spaces. Acta. Math inform. Univ, Ostrav 1, 5-11 (1993).
12. S. Sedghi, N. shobe, H. Zhan: A common fixed point thoerem in D-metric space, Fixed point theory Appl : [2007] -1-13 in article.
13. S. Sedghi, K. P. R. Rao, N.V.S. Shobe: Common fixed point theorems for six weekly compatible mappings in D – metric spaces, International J.Math. Math. Sci. 6 [2007] – 223- 237.
14. S. Sedghi, N.Shobe, A.Aliouche: A generalization of fixed point theorems in S-metric spaces. Mat , VESN 64, 258 – 266 [2012].
15. S. Sedghi, I.Altun, N.Shobe, M.Salahshour: Some properties of S-matric space and fixed points results Kyungpook math J-54, 113-122 [2014], doi 10.5666/KMJ.2014. 54.1.113.
16. S. Sedghi, N.Shobe, T.Dosenovic: Fixed point results in S-metric spaces - non – linear functional Anal. Appl. 20(1), 55 – 67 [2015].
17. S. Sedghi, A.Gholidahne, T.Dosenovic, J.Esfahani, S.Randenovic: Common fixed point of four maps in Sb -Metric Spaces-J. Linear Topol. Algebra 5(2),93-104(2016).
18. Z.Mustafa. B.Sims: A new approach to generalized Metric Space. J. non linear convex Anal 7 (2) -289-297 (2006).
19. ZMusthafa, B.Sims: Fixed point theorem for contractive mapings in complete G-metric spaces, fixed point theory and contractions, vol. 2009, Article ID 917175, 10 pages.
20. Z.Mustafa, TR.Roshan,. V.Parvaneh, Z. Kadelburg: Some Common fixed point results in ordered partial b-Metric space J. Iverurer. Appt 2013, 562 (2013).
21. Z.Mustafa, H.Huang. S.Randenovic: Some remarks on the paper “Some fixed point generalizations are not real generalizations.” I. Adv. Math Stud. 9 (1),110-116 (2016).

Citation :

K.P.R. Sastry, K.K.M. Sarma, P. Krishna Kumari, "Fixed Point Theorems for 𝜓 − 𝜑 − 𝜆 Contractions in 𝑆𝑏 − Metric Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 1, pp. 28-39, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P505