SOLVABILITY TO COUPLED SYSTEMS OF FUNCTIONAL EQUATIONS VIA FIXED POINT THEORY

Year 2018, Volume: 8 Issue: 1.1, 230 - 237, 01.09.2018

H. Işık

Abstract

The purpose of the present paper is to establish the existence and uniquness of coupled common xed points for a pair of mappings satisfying F-contraction. As a consequence of our results, we discuss the existence of a unique common solution of coupled systems of functional equations arising in dynamic programming.

Keywords

coupled common xed point , F-contraction , metric space , coupled system of functional equation.

References

• Ansari,A.H., I¸sık,H. and Radenovi´c,S., (2017), Coupled fixed point theorems for contractive mappings involving new function classes and applications, Filomat, 31(7), pp. 1893–1907.
• Banach,S., (1922), Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fundam. Math., 3, 133-181.
• Bellman,R. and Lee,E.S., (1978), Functional equations in dynamic programming, Aequ. Math., 17(1), pp. 1-18.
• Bhaskar,T.G. and Lakshmikantham,V., (2006), Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65, pp. 1379–1393.
• Dhage,B.C., O’Regan,D. and Agarwal,R.P., (2003), Common fixed point theorems for a pair of count- ably condensing mappings in ordered Banach spaces, Journal of Applied Mathematics and Stochastic Analysis, 16(3), pp. 243–248.
• Ding,H.S., Li,L. and Long,W., (2013), Coupled common fixed point theorems for weakly increasing mappings with two variables, J. Comput. Anal. Appl., 15(8), pp. 1381-1390.
• Guo,D. and Lakshmikantham,V., (1987), Coupled fixed points of nonlinear operators with applica- tions, Nonlinear Anal., 11, pp. 623-632.
• Harjani,J., Rocha,J. and Sadarangani,K., (2014), α-Coupled fixed points and their application in dynamic programming, Abstr. Appl. Anal., 2014, pp. 1-4.
• I¸sık,H. and T¨urko˘glu,D., (2014), Coupled fixed point theorems for new contractive mixed monotone mappings and applications to integral equations, Filomat, 28(6), pp. 1253-1264.
• I¸sık,H. and Radenovi´c,S., A new version of coupled fixed point results in ordered metric spaces with applications, To appear in U.P.B. Sci. Bull., Series A.
• Klim,D. and Wardowski,D., (2015), Fixed points of dynamic processes of set-valued F-contractions and application to functional equations, Fixed Point Theory Appl., 2015:22, pp. 1-9.
• Lakshmikantham,V. and ´Ciri´c,Lj., (2009), Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70, pp. 4341-4349.
• Opoitsev,V.I., (1975), Heterogenic and combined-concave operators, Syber. Math. J., 15, pp. 781–792 (in Russian).
• Opoitsev,V.I., (1975), Dynamics of collective behavior, III. Heterogenic system, Avtomat. i Telemekh., 36, pp. 124–138 (in Russian).
• Radenovi´c,S., (2014), Coupled fixed point theorems for monotone mappings in partially ordered metric spaces, Krag. J. Math., 38(2), pp. 249-257.
• Sgroi,M. and Vetro,C., (2013), Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat, 27(7), pp. 1259–1268.
• Shukla,S. and Radenovi´c,S., (2013), Some common fixed point theorems for F -contraction type map- pings in 0-complete partial metric spaces, Journal of Mathematics, Article ID 878730, pp. 1-7.
• Shukla,S., Radenovi´c,S. and Kadelburg,Z., (2014), Some fixed point theorems for F -generalized con- tractions in 0-orbitally complete partial metric spaces, Theory Appl. Math. Comput. Sci., 4(1), pp. 87-98.
• Wardowski,D., (2012), Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, pp. 1-6.
• Wardowski,D. and Van.Dung,N., (2014), Fixed points of F -weak contractions on complete metric spaces, Demonst. Math., 47(1), pp. 146-155.