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

Year 2020, Volume: 4 Issue: 3, 121 - 131, 31.08.2020

Milanka Gardasevic-filipovic Katarina Kukic Zoran Mitrovic , Stojan Radenovic

https://doi.org/10.31197/atnaa.632514

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

References

• [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] 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] 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] 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] 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] Sz. Andras, Fiber Picard operators and convex contractions, Fixed Point Theory,2003, 4, pp. 121-129
• [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] 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] 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] 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] T. Dosenovic, S. Radenovic, S. Sedghi, Generalized Metric Spaces: Survey, TWMSJ. Pure Appl. Math. V. 9, N.1, 2018, pp. 3-17
• [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] 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] F. Georgescu, IFSs consisting of generalized convex contractions, An. St. Univ. Ovidius Constanta, vol. 25 (1), 2017, 77-86
• [15] R. H. Haghi, S. Rezapour, N. Shahzad, Be careful on partial metric fixed point results,Topology Appl. 160 (3), (2013), 450-454
• [16] V. I. Istratescu, Some fixed point theorems for convex contraction mappings andconvex non-expansive mapping, Libertas Mathematica, 1981 (1), pp. 151-163
• [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] 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] W.A. Kirk, and N. Shahzad, Fixed Point Theory in Distance Spaces, 2014, SpringerInternational Publishing Switzerland 2014
• [20] S. G. Matthews, Metric domains for completeness technical report 76, PhD Thesis,Department of Computer Science, Univertsity of Warwick, Conventry, (1986).
• [21] M. A. Miandaragh, M. Postolache, S. Rezapour, Aproximate fixed points of generalized convex contractions, Fixed Point Theory Appl. 2013, 2013:255
• [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] 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] Z. Mustafa, B. Sims Some remarks concerning D-metric spaces, International Conference on Fixed Point Theory and Applications, Yokohama, Japan, 10 (2004)
• [25] A. Pant, R.P. Pant Fixed points and continuity of contractive maps, Filomat 31(11),3501-3506 (2017)
• [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] M. Ramezani, Orthogonal metric space and convex contractions, Int. J. NonlinearAnal. Appl. 6 (2015) No. 2, 127-132
• [28] B. E. Rhoades, Comparison of Various Definitions of Contractive Mappings, Transactions of the American Mathematical Society, 1977, 226, pp. 257-290
• [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] 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] 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] 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