In this article, we use the concept of proximity spaces to prove common fixed point results for mappings satisfying generalized ($ \psi $, $ \beta $)-Geraghty contraction type mapping in partially ordered proximity spaces. Finally, we investigate an application to endorse our results.
Citation: Demet Binbaşıoǧlu. Some fixed pointresults for nonlinear contractive conditions in ordered proximity spaceswith an application[J]. AIMS Mathematics, 2023, 8(6): 14541-14557. doi: 10.3934/math.2023743
In this article, we use the concept of proximity spaces to prove common fixed point results for mappings satisfying generalized ($ \psi $, $ \beta $)-Geraghty contraction type mapping in partially ordered proximity spaces. Finally, we investigate an application to endorse our results.
| [1] | F. Riesz, Stetigkeit und abstrakte mengenlehre, Rom. Math. Congr., 2 (1908), 18–24. |
| [2] | V. A. Efremovich, Infinitesimal spaces, Dokl. Akad. Nauk. SSSR, 76 (1951), 341–343. |
| [3] | M. Kula, S. Özkan, T. Maraşlı, Pre-Hausdorff and Hausdorff proximity spaces, Filomat, 31 (2017), 3837–3846. |
| [4] | M. Kula, S. Özkan, Regular and normal objects in the category of proximity spaces, Kragujev. J. Math., 43 (2019), 127–137. |
| [5] | Y. M. Smirnov, On proximity spaces, Mat. Sb., 31 (1952), 543–574. |
| [6] | Y. M. Smirnov, On the completeness of proximity spaces, Dokl. Akad. Nauk SSSR, 88 (1953), 761–764. |
| [7] | O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Jpn., 44 (1996), 381–391. |
| [8] | A. Kostic, $w$-distances on proximity spaces and a fixed point theorem, In: The third International Workshop on Nonlinear Analysis and its Applications, 2021. |
| [9] | R. Babaei, H. Rahimi, M. Sen, G. S. Rad, $w$-$b$-cone distance and its related results: A survey, Symmetry, 12 (2020), 171. |
| [10] | S. A. Naimpally, B. D. Warrack, Proximity Spaces, Cambridge: Cambridge University Press, 1970. |
| [11] | P. L. Sharma, Two examples in proximity spaces, Proc. Am. Math. Soc., 53 (1975), 202–204. |
| [12] |
M. Qasim, H. Aamri, I. Altun, N. Hussain, Some fixed point theorems in proximity spaces with applications, Mathematics, 10 (2022), 1724. https://doi.org/10.3390/math10101724 doi: 10.3390/math10101724
|
| [13] | M. Geraghty, On contractive mappings, Proc. Am. Math. Soc., 40 (1973), 604608. |
| [14] |
M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30, (1984), 1–9. https://doi.org/10.1017/S0004972700001659 doi: 10.1017/S0004972700001659
|
| [15] | H. Alsamir, M. S. M. Noorani, W. Shatanawi, K. Abodyah, Common fixed point results for generalized $(\psi, \beta)$-Geraghty contraction type mapping in partially ordered metric-like spaces with application, Filomat, 31 (2017), 5497–5509. |
| [16] |
H. A. Hammad, M. Zayed, Solving a system of differential equations with infinite delay by using tripled fixed point techniques on graphs, Symmetry, 14 (2022), 1388. https://doi.org/10.3390/sym14071388 doi: 10.3390/sym14071388
|
| [17] |
H. A. Hammad, M. De la Sen, Analytical solution of Urysohn integral equations by fixed point technique in complex valued metric spaces, Mathematics, 7 (2019), 852. https://doi.org/10.3390/math7090852 doi: 10.3390/math7090852
|
| [18] |
H. A. Hammad, P. Agarwal, S. Momani, F. Alsharari, Solving a fractional-order differential equation using rational symmetric contraction mappings, Fractal Fract., 5 (2021), 159. https://doi.org/10.3390/fractalfract5040159 doi: 10.3390/fractalfract5040159
|
Demet Binbaşıoǧlu. Some fixed point results for nonlinear contractive conditions in ordered proximity spaces with an application[J]. AIMS Mathematics, 2023, 8(6): 14541-14557. doi: 10.3934/math.2023743
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