SOME NEW FIXED POINT RESULTS FOR CONVEX CONTRACTIONS IN B-METRIC SPACES
Abstract
The purpose of this paper is to consider various results for convex contraction mappings in the context of B-metric spaces. We, among other things, generalize, extend, correct and enrich the recent published results from the context of convex contractions defined on an ordinary metric spaces to the ones on the so-called B-metric spaces. One example shows that this generalization is genuine. Let us note that this paper represents only the beginning of our investigation of the properties of convex contractions observed in any general metric space.
In the papers that are to be published, our considerations are applied to cone metric spaces, partial metric spaces, G-metrics, GB-metrics, extended B-metric spaces and many others.
References
Aleksić, S., Došenović, T., Mitrović, Z., & Radenović, S. 2019a. Remarks on common fixed point results for generalized α*-ψ contraction multivalued mappings in b-metric spaces, Adv. Fixed Point Theory, 9 (1), pp. 1-16.
Aleksić, S., Kadelburg, Z. T., Mitrović, Z., & Radenović, S. 2019b. A new survey: Cone metric spaces. Journal of the International Mathematical Virtual Institute, 9, pp. 93-121.
Aleksić, S. T., Mitrović, Z., & Radenović, S. 2019c. Picard sequences in b-metric spaces, too appear in Fixed point Theory 2019-2020.
Alnafei, S. H., Radenović, S., & Shahzad, N. 2011. Fixed point theorems for mappings with convex diminishing diameters on cone metric spaces. Applied Mathematics Letters, 24(12), pp. 2162-2166. doi:10.1016/j.aml.2011.06.019
Ampadu, C. K. 2017. On the analogue of the convex contraction mapping theorem for tri-cyclic convex contraction mappings of order 2 in b-metric space. J. Global Research Math. Archives, 4(6), pp. 1-5.
Ampadu, C. B. 2018. Some Fixed Point Theory Results For Convex Contraction Mapping Of Order 2. JP Journal of Fixed Point Theory and Applications, 12(2-3), pp. 81-130. doi:10.17654/fp0120230081
Andras, Sz. 2003. Fiber Picard operators and convex contractions. Fixed Point Theory, 4, pp. 121-129.
Bakhtin, I. A. 1989. The contraction mapping principle in quasimetric spaces. Funct. Anal, 30, pp. 26-37.
Collaço, P., & Silva J. C. 1997. A complete comparison of 25 contraction conditions. Nonlinear Analysis: Theory, Methods and Applications, 30(1), pp. 471-476. doi:10.1016/s0362-546x(97)00353-2
Istratescu, V. I. 1981. Some fixed point theorems for convex contraction mappings and convex non-expansive mapping (I). Libertas Mathematica, 1, pp. 151-163.
Istraţescu, V. I. 1982. Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters. — I. Annali di Matematica Pura ed Applicata, 130(1), pp. 89-104. doi:10.1007/bf01761490
Istraţescu, V. I. 1983. Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters, II. Annali di Matematica Pura ed Applicata, 134(1), pp. 327-362. doi:10.1007/bf01773511
Jeong, G. S., & Rhoades, B. E. 2005. Maps for which F(T)=F(T^n). Fixed Point Theory Appl, 6, pp. 71-105.
Kirk, W. A., Srinivasan, P. S., & Veeramani, P. 2003. Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory, 4, pp. 79-89.
Kirk, W., & Shahzad, N. 2014. Fixed Point Theory in Distance Spaces.Cham: Springer Science and Business Media LLC. doi:10.1007/978-3-319-10927-5
Rhoades, B. E. 1977. A comparison of various definitions of contractive mappings. Transactions of the American Mathematical Society, 226, pp. 257-257. doi:10.1090/s0002-9947-1977-0433430-4
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.