Fixed Point Results for φ - (γ, η, n, m)-Contractions with Applications to Nonlinear Integral Equations

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Hasanen A. Hammad, Manuel De la Sen, Fixed Point Results for φ - (γ, η, n, m)-Contractions with Applications to Nonlinear Integral Equations, Int. J. Anal. Appl., 17 (3) (2019), 448-463.

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Hasanen A. Hammad, Manuel De la Sen

Abstract

The aim of this paper is to introduce a new class of pair of contraction mappings, called φ - (γ, η, n, m)-contraction pairs, and obtain common fixed point theorems for a pair of mappings in this class, satisfying a weakly compatible condition. As an application, we use mappings of this class to find the existence of solutions for nonlinear integral equations on the space of continuous functions and in some of its subspaces. Moreover, some examples are given here to illustrate the applicability of these results.

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References

  1. M. Berzig, S. Chandok and 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 and C. Vetro, Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation, Appl. Math. Comput., 232 (2014), 955-967.
  3. Z. Liu, X. Li, S. Minkan and S.Y. Cho, Fixed point theorems for mappings satisfying contractive condition of integral type and applications, Fixed Point Theory and Appl., 2011 (2011), Art. ID 64.
  4. H. K. Pathak, M.S. Khan and R. Tiwari, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl., 53 (2007), 961-971.
  5. S. Radenovi ´c, T. Doˇsenovi ´c, T. A. Lampert and Z. Golubov ´i ´c, A note on some recent fixed point results for cyclic contractions in b-metric spaces and an application to integral equations, Appl. Math. Comput., 273 (2016), 155-164.
  6. N. Shahzad, O. Valero and M.A. Alghamdi, A fixed point theorem in partial quasi-metric spaces and an application to software engineering, Appl. Math. and Comput., 268 (2015), 1292-1301.
  7. N. Hussain and M. A. Taoudi, Krasnoselskii-type fixed point theorems with applications to Volterra integral equations, Fixed Point Theory Appl., 2013 (2013), Art. ID 196.
  8. G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9(4) (1986), 771-779.
  9. R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl., 240 (1999), 284-289.
  10. M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strictly contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188.
  11. W. Sintunavarat and P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011 (2011), Art. ID 637958.
  12. G. Jungck, Common fixed point for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci., 4(2) (1986), 199-215.
  13. G. U. R. Babu and P. D. Sailaja, A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai J. Math., 9(1) (2011), 1-10.
  14. L. Nikolova and S. Varoˇsanec, Properties of some functionals associated with h-concave and quasilinear functions with applications to inequalities, J. Inequal. Appl. 2014 (2014), Art. ID 30.