Coupled Coincidence Point for f(ψ, φ)-Contractions via Generalized α-Admissible Mappings with an Application

Main Article Content

Dhekra M. Albaqeri
Hasanen A. Hammad
Manuel De La Sen

Abstract

The main objective of this manuscript is to discuss some coupled coincidence point (ccp) results for generalized α- admissible mappings which are f(ψ, φ)- contractions in the context of b-metric spaces (b-ms). Also, an example to support the obtained theoretical theorems is derived. Ultimately, an analytical solution for nonlinear integral equation (nie) is discussed as an application.

Article Details

References

  1. M. Berzig, S. Chandok, M.S. Khan, Generalized Krasnoselskii fixed point theorem involving auxiliary functions in bimetric spaces and application to two-point boundary value problem, Appl. Math. Comput. 248 (2014), 323-327.
  2. D. Gopal, M. Abbas, C. Vetro, Some new fixed point theorems in manger PM-spaces with application to Volterra type integral equation, Appl. Math. Comput. 232 (2014), 955-967.
  3. Z. Liu, X. Li, S.M. Kang, S.Y. Cho, Fixed point theorems for mappings satisfying contractive condition of integral type and applications, Fixed Point Theory Appl. 2011 (2011), 64.
  4. H.K. Pathak, M.S. Khan, R. Tiwari, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. 53 (2007), 961-971.
  5. H.A. Hammad, M. De la Sen, A Solution of Fredholm integral equation by using the cyclic r q s-rational contractive mappings technique in b-metric-like spaces, Symmetry, 11 (2019), 1184.
  6. H. A. Hammad, M. De la Sen, Solution of nonlinear integral equation via fixed point of cyclic α q s-rational contraction mappings in metric-like spaces, Bull. Braz. Math. Soc. New Ser. 51 (2020), 81-105.
  7. N. Shahzad, O. Valero, M.A. Alghamdi, A fixed point theorem in partial quasi-metric spaces and an application to software engineering, Appl. Math. Comput. 268 (2015), 1292-1301.
  8. N.Hussain, M.A. Taoudi, Krasnoselskii-type fixed point theorems with applications to Volterra integral equations, Fixed Point Theory Appl. 2013, (2013), 196.
  9. I.A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal. 30 (1989) 26-37.
  10. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav. 1 (1993), 5-11.
  11. A. Aghajani, M. Abbas, J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (4) (2014), 941-960.
  12. R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 2153-2163.
  13. M. Shah, S. Simic, N. Hussain, A. Sretenovic, S. Radenovi ´c, Common fixed points theorems for occasionally weakly compatible pairs on cone metric type spaces, J. Comput. Anal. Appl. 14 (2012), 290-297.
  14. N. Hussain, M. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl. 62 (2011), 1677-1684.
  15. M. Khamsi and N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., Theory Meth. Appl. 73 (2010), 3123-3129.
  16. S. Radenovic, K. Zoto, N. Dedovic, V. Sesum-Cavic, A. Ansari, Bhaskar-Guo-Lakshmikantam-Ciric type results via new functions with applications to integral equations, Appl. Math. Comput. 357 (2019), 75-87.
  17. D. Guo, V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal., Theory Meth. Appl. 11 (1987), 623-632.
  18. T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., Theory Meth. Appl. 65 (2006), 1379-1393.
  19. M. Abbas, M.A. Khan, S. Radenovi ´c, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput. 217 (2010), 195-202.
  20. H. Aydi, M. Postolache, W. Shatanawi, Coupled fixed point results for (ψ, φ)-weakly contractive mappings in ordered G-metric spaces, Comput. Math. Appl. 63 (2012), 298-309.
  21. V. Berinde, Coupled fixed point theorems for contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal., Theory Meth. Appl. 75 (2012), 3218-3228.
  22. B.S. Choudhury, P. Maity, Coupled fixed point results in generalized metric spaces, Math. Comput. Model. 54 (2011), 73-79.
  23. H.A. Hammad, M. De la Sen, A coupled fixed point technique for solving coupled systems of functional and nonlinear integral equations, Mathematics, 7 (2019), 634.
  24. H.A. Hammad, D.M. Albaqeri, R.A. Rashwan, Coupled coincidence point technique and its application for solving nonlinear integral equations in RPOCbML spaces, J. Egypt. Math. Soc. 28 (2020), 8.
  25. N. Hussain, M. Abbas, A. Azam, J. Ahmad, Coupled coincidence point results for a generalized compatible pair with applications, Fixed Point Theory Appl. 2014 (2014), 62.
  26. H.A. Hammad, H. Aydi, M. De la Sen, Generalized dynamic process for an extended multi-valued F-contraction in metriclike spaces with applications, Alex. Eng. J. 59 (2020), 3817-3825.
  27. V. Lakshmikantham, Lj. B. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. Theory Methods Appl. 70, (2009), 4341-4349.
  28. H. Alsulami, S. Gulyaz, E. Karapinar, I.M. Erhan, Fixed point theorems for a class of α- admissible contractions and applications to boundary value problem, Abstr. Appl. Anal. 2014 (2014), Article ID 187031.
  29. A.H. Ansari, S. Chandok, C. Ionescu, Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions, J. Inequal. Appl. 2014 (2014), 429.