Applications of Fixed Point Theory in Integral Equations and Homotopy Using Partially Ordered S_b Metric Spaces

  • Authors

    • D Ram Prasad
    • GNV Kishore
    • K Priyanka
    2018-06-21
    https://doi.org/10.14419/ijet.v7i3.3.14509
  • metric space · −Cauchy sequence · -completeness · fixed point · Suzuki type contraction

  • In this paper we give some applications to integral equations as well as homotopy theory via Suzuki  type fixed point theorems in partially ordered complete  - metric space by using generalized contractive conditions. We also furnish an example which supports our main result.

     

     

  • References

    1. [1] Abbas M, Ali khan M and Randenovic S, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl.Math. Comput.,217, (2010),195-202.

      [2] Banach S, Theorie des Operations lineaires, Manograic Mathematic Zne, Warsaw, Poland, 1932.

      [3] Czerwik S, Contraction mapping in b-metric spaces, Acta Mathematica et Informatica Universitatis

      [4] Ostraviensis, 1 (1993), 5 - 11.

      [5] Kishore G.N.V, Rao K. P. R and Hima Bindu V.M.L, Suzuki type unique common fixed point theorem in

      [6] partial metric spaces by using (C): condition with rational expressions, Afr. Mat. (2016),

      [7] DOI 10.1007/s13370-017-0484-x

      [8] Lakshmikantham V, ´Ciri´c Lj, Coupled fixed point theorems for nonlinear contractions in partially

      [9] ordered metric spaces, Nonlinear Analysis. Theory, Methods and Applications, 70(12),(2009),4341-4349.

      [10] Mustafa Z, Sims B, A new approach to generalized metric spaces, J Nonlinear Convex Anal, 7(2),(2006), 289-297.

      [11] Rohen Y, Doˇsenovi´c T, Radenovi´c S, A note on the paper â€A fixed point theorems in −metric spaces†acceptet in Filomat.

      [12] Sedghi S, Altun I, Shobe N and Salahshour M, Some properties of S-metric space and fixed point results, Kyung Pook Math. J., 54(2014), 113 - 122. Applications via fixed point results ... 15

      [13] Sedghi S, Gholidahneh, Doˇsenovi´c T, Esfahani J and Radenovic S, Common fixed point of four maps in -metric spaces, Journal of Linear and Topological Algebra, Vol.5(2), (2016), 93 - 104.

      [14] Sedghi S, Shobe N and Aliouche A, A generalization of fixed point theorem in S-metric spaces, Mat. Vesnik, 64 (2012), 258-266.

      [15] Sedghi S, Shobe N and T.Doˇsenovi´c, Fixed point results in S-metric spaces, Nonlinear Functional Analysis and Applications, 20(1), (2015), 55-67.

      [16] Sedghi S, Rezaee M.M, Doˇsenovi´c T, Radenovi´c S, Common fixed point theorems for contractive mappings satisfying _-maps in S-metric spaces, Acta Univ. Sapientiae, Mathematica, 8(2), (2016), 298-311.

      [17] .Gholidahneh A, Sedghi S, Doˇsenovi´c T, Radenovi´c S, Ordered S-metric Spaces and Coupled Common Fixed Point Theorems of Integral Type Contraction, Mathematics Interdisciplinary Research 2 (2017), 71 - 84.

  • Downloads

  • How to Cite

    Ram Prasad, D., Kishore, G., & Priyanka, K. (2018). Applications of Fixed Point Theory in Integral Equations and Homotopy Using Partially Ordered S_b Metric Spaces. International Journal of Engineering & Technology, 7(3.3), 146-150. https://doi.org/10.14419/ijet.v7i3.3.14509