New generalization of Darbo’s fixed point theorem via \(\alpha\)-admissible simulation functions with application. (English) Zbl 1474.54201
Summary: In this paper, at first, we introduce \(\alpha_{\mu}\)-admissible, \(Z_\mu\)-contraction and \(N_{\mu}\)-contraction via simulation functions. We prove some new fixed point theorems for defined class of contractions via \(\alpha\)-admissible simulation mappings, as well. Our results can be viewed as extension of the corresponding results in this area. Moreover, some examples and an application to functional integral equations are given to support the obtained results.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
Keywords:
measure of non-compactness; simulation functions; \(\alpha\)-admissible mappings; fixed pointReferences:
| [1] | A. Aghajani, J. Bana´s and N. Sabzali,Some generalizations of Darbo’s fixed point theorem and applications, Bull. Belg. Math. Soc., Simon Stevin 20 (2013), pp. 345-358. · Zbl 1290.47053 |
| [2] | J. Bana’s and K. Goebel,Measures of noncompactness in Banach spaces, in: Lecture Notes in Pure and Applied Mathematics, Dekker New York, 60, 1980. · Zbl 0441.47056 |
| [3] | J. Chen and X. Tang,Generalizations of Darbo’s fixed point theorem via simulation functions with application to functional integral equations, J. Comput. Appl. Math., 296 (2016), pp. 564-575. · Zbl 1329.47054 |
| [4] | C.-M. Chen, E. Karapınar and D. O’regan,On(α−ϕ)-Meir-Keeler contractions on partial Hausdorff metric spaces, University Politehnica Of Bucharest Scientific, Bulletin-Series A-Applied Mathematics And Physics, 80 (2018), pp. 101-110. · Zbl 1438.54113 |
| [5] | G. Darbo,Punti unitti in transformazioni a condominio non compatto, Rend. Semin. Mat. Univ. Padova, 24 (1955), pp. 84-92. · Zbl 0064.35704 |
| [6] | A. Farajzadeha and A. Kaewcharoen,Best proximity point theorems for a new class ofα−ψ−proximal contractive mappings, J. Non. Conv. Anal. 16 (2015), pp. 497-507. · Zbl 1311.54039 |
| [7] | A. Farajzadeha, P. Chuadchawna and A. Kaewcharoen,Fixed point theorems for(α;η;ψ;ξ)−contractive multi-valued mappings onα− ηcomplete partial metric spaces, J. Nonlinear Sci. Appl., 9 (2016), pp. 1977-1990. · Zbl 1338.54163 |
| [8] | M. Geraghty,On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), pp. 604-608. · Zbl 0245.54027 |
| [9] | L. Gholizadeh and E. Karapınar,Best proximity point results in dislocated metric spaces viaR-functions, Revista da la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matem´aticas, 112 (2018), pp. 1391-1407. · Zbl 1425.54024 |
| [10] | A. Hajji,A generalization of Darbo’s fixed point and common solutions of equations in Banach spaces, Fixed Point Theory Appl. (2013), 2013:62. · Zbl 1364.47007 |
| [11] | E. Karapınar and F. Khojasteh,An approach to best proximity points results via simulation functions, J. Fixed Point Theory Appl. 19 (2017), pp. 1983-1995. · Zbl 1489.54154 |
| [12] | M. S. Khan, M. Swaleh and S. Sessa,Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30 (1984), pp. 1-9. · Zbl 0553.54023 |
| [13] | F. Khojasteh, S. Shukla and S. Radenovic,A new approach to the study of fixed point theory for simulation function, Filomat, 29 (2015), pp. 1189-1194. · Zbl 1462.54072 |
| [14] | O. Popescu,Some new fixed point theorems forα-Geraghty contractive type maps in metric spaces, Fixed Point Theory Appl., (2014), 2014:190. · Zbl 1451.54020 |
| [15] | A.F. Rold´an-L´opez-de-Hierro, E. Karapınar, C. Rold´an-L´opez-deHierro and J. Martnez-Moreno,Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), pp. 345-355. · Zbl 1318.54034 |
| [16] | A. Samadi and M.B. Ghaemi,An extension of Darbo’s theorem and its application, Abstr. Appl. Anal., 2014 (2014), Article ID 852324, 11 pages. · Zbl 1473.47018 |
| [17] | B. Samet, C. Vetro and P. Vetro,Fixed point theorem forα−ψcontractive type mappings, Nonlinear Anal., 75 (2012), pp. 21542165. · Zbl 1242.54027 |
| [18] | P. Zangenehmehr, A.P. Farajzadeh and S.M. Vaezpour,On fixed point theorems for monotone increasing vector valued mappings via scalarizing, Positivity, 19 (2015), pp. 333-340. · Zbl 1319.47047 |
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