Fixed points for \(\alpha- \beta_E\)-Geraghty contractions on \(b\)-metric spaces and applications to matrix equations. (English) Zbl 1491.54047
Summary: In this paper, we introduce the notion of \(\alpha - \beta_E\)-Geraghty contraction type mappings on \(b\)-metric spaces and prove the existence and uniqueness of fixed point for such mappings. These results are generalizations of the recent results in [A. Fulga and A. M. Proca, J. Nonlinear Sci. Appl. 10, No. 9, 5125–5131 (2017; Zbl 1412.47118)]. We give some examples illustrating the presented results. An application on matrix equations and numerical algorithms are also provided.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
| 15A24 | Matrix equations and identities |
Citations:
Zbl 1412.47118References:
| [1] | T. Abdeljawad, N. Mlaiki, H. Aydi, N. Souayah, Double controlled metric type spaces and some fixed point results, Mathematics, 2018, 6(12), 320. · Zbl 1425.47017 |
| [2] | H. Afshari, H. Aydi, E. Karapinar, On generalizedα−ψ-Geraghty contractions onb-metric spaces, Georgian Mathematical Journal, https://doi.org/10.1515/gmj-2017-0063, (2018). · Zbl 1437.54035 |
| [3] | E. Ameer, H. Aydi, M. Arshad, H. Alsamir, M.S. Noorani, Hybrid multivalued type contraction mappings inαK-complete partial b-metric spaces and applications, Symmetry, 2019, 11(1), 86. · Zbl 1423.47015 |
| [4] | H. Aydi, A. Felhi, E. Karapinar, S. Sahmim, A Nadler-type fixed point theorem in dislocated spaces and applications, Miscolc Math. Notes, 19 (1) (2018), 111-124. · Zbl 1474.54118 |
| [5] | H. Aydi, W. Shatanawi, C. Vetro, On generalized weakly G-contraction mapping in G-metric spaces, Comput. Appl. 62 (2011), 4222-4229. · Zbl 1236.54036 |
| [6] | H. Aydi, A. Felhi, H. Afshari, New Geraghty type contractions on metric-like spaces, J. Nonlinear Sci. Appl, 10 (2) (2017), 780-788. · Zbl 1412.47098 |
| [7] | H. Aydi, E. Karapinar, P. Salimi, I.M. Erhan, Best proximity points of generalized almostψ-Geraghty contractive non-self mappings, Fixed Point Theory Appl. 2014, 2014:32. · Zbl 1333.54043 |
| [8] | M. Berzig, B. Samet, Solving systems of nonlinear matrix equations involving Lipshitzian mappings, Fixed Point Theory Appl. 2011, 2011:89. · Zbl 1272.15011 |
| [9] | D.H. Cho, J.D. Bae, E. Karapinar, Fixed point theorems forα-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. 2013, Article ID 329 (2013). · Zbl 1423.54073 |
| [10] | S. Czerwik, Nonlinear set-valued contraction mappings inb-metric spaces, Atti Semin. Mat. Fis. Univ. Modena 46 (2) (1998), 263-276. · Zbl 0920.47050 |
| [11] | D. Duki´c, Z. Kadelburg, S. Radenovi´c, Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstract and Applied Analysis, 2011 (2011), 13 pages. · Zbl 1231.54030 |
| [12] | A. Fulga, A.M. Proca, Fixed points forϕE-Geraghty contractions, J. Nonlinear Sci. Appl. 10 (2017), 51255131. · Zbl 1412.47118 |
| [13] | M. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40 (1973), 604-608. · Zbl 0245.54027 |
| [14] | M.S. Khan, M. Berzig, B. Samet, Some convergence results for iterative sequences of Presic type and applications, Advances in Difference Equations, 2012, 2012:38. · Zbl 1444.54029 |
| [15] | E. Karapinar, R.P. Agarwal, H. Aydi, Interpolative Reich-Rus- ´Ciri´c type contractions on partial metric spaces, Mathematics, 2018, 6, 256. · Zbl 1469.54127 |
| [16] | Y. Lim, Solving the nonlinear matrix equationX=Q+Pmi=1MiXδM∗ivia a contraction principle, Linear Algebra Appl, 430 (2009), 1380-1383. · Zbl 1162.15008 |
| [17] | Z. Mustafa, H. Aydi, E. Karapinar, On common fixed points in G-metric spaces using (E.A) property, Comput. Math. Appl. 6 (2012), 1944-1956. · Zbl 1268.54027 |
| [18] | 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. · Zbl 1383.54048 |
| [19] | R. Nussbaum, Hilbert’s projective metric and iterated nonlinear maps. Mem. Amer.Math. Soc. 75 (391) (1988), 1-37. · Zbl 0666.47028 |
| [20] | R. Nussbaum, Finsler structures for the part metric and Hilbert’ projective metric and applications to ordinary differential equations, Differ. Integral Equ. 7 (1994), 1649-1707. · Zbl 0844.58010 |
| [21] | P. Patle, D. Patel, H. Aydi, S. Radenovi´c, OnH+-type multivalued contractions and applications in symmetric and probabilistic spaces, Mathematics, 2019, 7(2), 144. |
| [22] | O. Popescu, Some new fixed point theorems forα-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. 2014 (190) (2014), 1-12. · Zbl 1451.54020 |
| [23] | S. Reich, A.J. Zaslavski, Monotone contractive mappings, J. Nonlinear Var. Anal. 1 (3) (2017), 391-401. · Zbl 1437.54066 |
| [24] | H. Qawaqneh, M.S. Noorani, W. Shatanawi, H. Aydi, H. Alsamir, Fixed point results for multi-valued contractions in b-metric spaces, Mathematics, 2019, 7(2), 132. · Zbl 1438.54111 |
| [25] | N. Tahat, H. Aydi, E. Karapinar, W. Shatanawi, Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces, Fixed Point Theory Appl. 2012, 2012 :48. · Zbl 1273.54078 |
| [26] | A. Thompson, On certain contraction mappings in a partially ordered vector space, Proc. Am. Math. Soc. 14 (1963), 438-443 · Zbl 0147.34903 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
