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SOLVABILITY TO COUPLED SYSTEMS OF FUNCTIONAL EQUATIONS VIA FIXED POINT THEORY

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

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.

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

Abstract

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.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

H. Işık This is me

Publication Date September 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 1.1

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