Best proximity point theorems for probabilistic proximal cyclic contraction with applications in nonlinear programming. (English) Zbl 1345.54068
Summary: In this paper, we derive a best proximity point theorem for non-self-mappings satisfied proximal cyclic contraction in PM-spaces and this shows the existence of optimal approximate solutions of certain simultaneous fixed point equations in the event that there is no solution. As an application we consider a nonlinear programming problem. Our results extend and improve the recent results of S. Sadiq Basha [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 17, 5844–5850 (2011; Zbl 1238.54021)].
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E70 | Probabilistic metric spaces |
| 54E40 | Special maps on metric spaces |
| 90C30 | Nonlinear programming |
Keywords:
optimal approximate solution; fixed point; best proximity point; proximal contraction; proximal cyclic contractionCitations:
Zbl 1238.54021References:
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| [2] | Hadžić, O, Pap, E: Fixed Point Theory in Probabilistic Metric Spaces. Mathematics and Its Applications, vol. 536. Kluwer Academic, Dordrecht (2001) |
| [3] | Hussain, N, Pathak, HK, Tiwari, S: Application of fixed point theorems to best simultaneous approximation in ordered semi-convex structure. J. Nonlinear Sci. Appl. 5(4), 294-306 (2012) (special issue) · Zbl 1432.41007 |
| [4] | Chauhan, S, Pant, BD: Fixed point theorems for compatible and subsequentially continuous mappings in Menger spaces. J. Nonlinear Sci. Appl. 7(2), 78-89 (2014) · Zbl 1477.54065 |
| [5] | Miheţ, D: Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces. J. Nonlinear Sci. Appl. 6(1), 35-40 (2013) · Zbl 1295.54066 |
| [6] | Sadiq Basha, S: Best proximity point theorems generalizing the contraction principle. Nonlinear Anal. 74(17), 5844-5850 (2011) · Zbl 1238.54021 · doi:10.1016/j.na.2011.04.017 |
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