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

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

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.

___

  • [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