Review of the convex contractions of Istratescu's type in various generalized metric spaces

Abstract

The main purpose of this paper is to consider convex contraction of Istratescu’s type in various generalized metric spaces (partial metric spaces, cone metric spaces, cone b-metric spaces, partial b-metric spaces, and others). In it, among other things, we generalize, extend, correct and enrich the recent announced results in existing literature.

Keywords

• Convex contraction,fixed point,b-metric space,cone metric space,S-metric space

Kaynakça

1. [1] R. P. Agarwal, E. Karapinar, D. O'Regan, A.F.R.L. -de Hierro, Fixed Point Theoryin Metric Type Spaces, Springer International Publishing Switzerland 2015
2. [2] S. Aleksic, Z. Kadelburg, Z. D. Mitrovic, S. Radenovic, A new survey: Cone metricspaces, Journal of the International Mathematical Virtual Institute, 2019, 9, pp.93-121
3. [3] M. A. Alghamdi, S. H. Alnafei, S. Radenovic, N. Shahzad, Fixed point theoremsfor mappings with convex diminishing diameters on cone metric spaces, Appl. Math.Let., 24 (2011) 2162-2166.
4. [4] M. A. Alghamdi, S. H. Alnafei, S. Radenovic, N. Shahzad, Fixed point theorems forconvex contraction mappings on cone metric spaces, Math. Comput. Model. 54 (2011)2020-2026
5. [5] C.K.Ampadu, Some fixed point theory results for convex contraction mapping of order2, JP Journal of Fixed Point Theory and Applications, Volume 12, Numbers (2-3),2017, Pages 81-130
6. [6] Sz. Andras, Fiber Picard operators and convex contractions, Fixed Point Theory,2003, 4, pp. 121-129
7. [7] H. Aydi, D. Rakic, A. Aghajani, T. Dosenovic, M.S. Noorani and H. Qawaqneh,On fixed point results in G b metric spaces, Mathematics 2019, 7, 617;doi:10.3390/math7070617.
8. [8] R. K. Bisht, V. Rakocevic, Fixed points of convex and generalized convex contractions, Rendiconti del Circolo Matematico di Palermo Series 2,https://doi.org/10.1007/s12215-018-0386-2

9. [9] R.K.Bisht, N. Hussain, A note on convex contraction mappings and discontinuity atfixed point, Journal of Mathematical Analysis, Volume 8, Issue 4 (2017), Pages 90-96
10. [10] D.Dj. Dolicanin, B. B. Mohsin, Some new fixed point results for convex contractionsin b-metric spaces, UNIVERSITY THOUGHT, Publication in Nature Sciences, Vol.9, No. 1, 2019
11. [11] T. Dosenovic, S. Radenovic, S. Sedghi, Generalized Metric Spaces: Survey, TWMSJ. Pure Appl. Math. V. 9, N.1, 2018, pp. 3-17
12. [12] N. V. Dung and V.T.L. Hanh, Remarks on partial b-metric spaces and fixed pointtheorems, Matematički Vesnik 22, 2, 2016, 151-164
13. [13] K. S. Eke, V. O. Olisama and S. A. Bishop, Some fixed point theorems for convex contractive mappings in complete metric spaces with applications, Cogent Mathematics & Statistics (2019)6: 1655870
14. [14] F. Georgescu, IFSs consisting of generalized convex contractions, An. St. Univ. Ovidius Constanta, vol. 25 (1), 2017, 77-86
15. [15] R. H. Haghi, S. Rezapour, N. Shahzad, Be careful on partial metric fixed point results,Topology Appl. 160 (3), (2013), 450-454
16. [16] V. I. Istratescu, Some fixed point theorems for convex contraction mappings andconvex non-expansive mapping, Libertas Mathematica, 1981 (1), pp. 151-163
17. [17] V. I. Istratescu, Some fixed point theorems for convex contraction mappings andmappings with convex diminishing diameters-I, Annali di Mat. Pura Appl., 1982,130, pp. 89-104
18. [18] V. I. Istratescu, Some fixed point theorems for convex contraction mappings andmappings with convex diminishing diameters-II, Annali di Mat. Pura Appl., 1983,130, pp. 327-362
19. [19] W.A. Kirk, and N. Shahzad, Fixed Point Theory in Distance Spaces, 2014, SpringerInternational Publishing Switzerland 2014
20. [20] S. G. Matthews, Metric domains for completeness technical report 76, PhD Thesis,Department of Computer Science, Univertsity of Warwick, Conventry, (1986).
21. [21] M. A. Miandaragh, M. Postolache, S. Rezapour, Aproximate fixed points of generalized convex contractions, Fixed Point Theory Appl. 2013, 2013:255
22. [22] R. Miculescu, A. Mihail, A generalization of Istratescu's fixed point theorem for convex contractions, Fixed Point Theory 18(2), (2017), 689-702
23. [23] R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl. 19, (2017), 2153-2163.
24. [24] Z. Mustafa, B. Sims Some remarks concerning D-metric spaces, International Conference on Fixed Point Theory and Applications, Yokohama, Japan, 10 (2004)
25. [25] A. Pant, R.P. Pant Fixed points and continuity of contractive maps, Filomat 31(11),3501-3506 (2017)
26. [26] S. Radenovic, Classical fixed point results in 0-complete partial metric spaces viacyclic-type extension, Bull. Allahabad Math. Soc. 31, 1, 2016, 39-55
27. [27] M. Ramezani, Orthogonal metric space and convex contractions, Int. J. NonlinearAnal. Appl. 6 (2015) No. 2, 127-132
28. [28] B. E. Rhoades, Comparison of Various Definitions of Contractive Mappings, Transactions of the American Mathematical Society, 1977, 226, pp. 257-290
29. [29] Y. Rohen, T. Dosenovic, S. Radenovic, A note on paper " A fixed point theorem inSb metric spaces", Filomat, 31:11, (2017), 3335-3346.
30. [30] N. Saleem, A. H. Ansari, M. Pavlovic, S. Radenovic, Some newq results in the framework of S b metric spaces, Scientic Publications of The State University of Novi Pazar, Ser. A. Appl. Math. Inform. and Mech. vol. 9, 2 (2017), 151-165
31. [31] S. Sedghi, A. Gholidahnen, T. Dosenovic, J. Esfahani, S. Radenovic, Common fixedpoint of four maps in S_b metric spaces, Journal of Linear and Topological Algebra,Vol. 05, No. 02, (2016), 93-104
32. [32] J. Vujakovic, H. Aydi, S. Radenovic, A. Mukheimer, Some remarks and newresults in ordered partial b-metric spaces, Mathematics, 2019, 7, 334, doi:10.3390/math7040334