EXISTENCE AND UNIQUENESS OF TRIPLED FIXED POINTS FOR MIXED MONOTONE OPERATORS WITH PERTURBATIONS AND APPLICATION

Year 2016, Volume: 6 Issue: 2, 213 - 223, 01.12.2016

Hojjat Afshari Alireza Kheiryan

Abstract

In this article, we get the existence and uniqueness of tripled fixed points without assuming the operator to be compact or continuous, which extends the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for a fractional differential equation boundary value problem.

Keywords

tripled fixed point, mixed monotone operator, positive solution, fractional differential equation.

References

• Berinde,V. and Borcut,M., (2012), Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput., 218(10), pp. 5929-5936.
• Liang,K., Li,J. and Xiao,T.J., (2005), New existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation, Comput. Math. Appl. 50, pp. 1569-1578. pp. 215- 224.
• Sabatier,J., Agrawal,O.P. and Machado,J.A.T., (2007), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht.
• Samko,S.G., Kilbas,A.A. and Marichev,O.I., (1993), Fractional Integral and Derivative:Theory and Applications, Gordan & Breach, Switzerland.
• Xu,X.J, Jiang,D.Q. and Yuan,C.J., (2009), Multiple positive solutions for the boundary value problems of a nonlinear fractional differential equation, Nonlinear Anal. TMA. 71, pp. 4676-4688.
• Sang,Y., (2013), Existence and uniqueness of fixed points for mixed monotone operators with pertur- bations, Electronic Journal of Differential Equations, 233, pp. 1-16.
• Sang,Y., (2013), A class of ϕ-concave operators and applications, Fixed Point Theory and Applica- tions, vol. 2013.