Fixed Point Theorems for Contractive Mappings in Probabilistic Modular Spaces

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Shahnaz Jafari, Maryam Shams, Asier Ibeas

Abstract

In this paper we introduce the concept of contractive maps and prove some related fixed point theorems in probabilistic modular spaces. In addition, we investigate the existence of common fixed points for a finite linear combination of contractive mappings. Finally, some results concerned with the convergence properties of sequences defined by contractive maps in probabilistic modular spaces are also given.

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References

  1. A. B. Amar, A. Jeribi, M. Mnif, Some fixed point theorems and application to biological model, Numer. Funct. Anal. Optim. 29 (1-2) (2008), 1-23.
  2. L. Marks, Fixed-point optimization of atoms and density in DFT, J. Chem. Theory Comput. 9 (6) (2013), 2786-2800.
  3. M. A. Khamsi, W. A. Kirk, An introduction to metric spaces and fixed point theory, vol. 53, Wiley, New York, 2011.
  4. L. B. Ciri ´c, B. Fisher, Fixed Point Theory: contraction mapping principle, Faculty of Mechanical Engineering, University ´ of Belgrade, Serbia, 2003.
  5. Z. Zuo, Some fixed point property for multivalued nonexpansive mappings in banach spaces, Math Inequal Appl. 7 (1) (2013), 129-137.
  6. K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. 28 (12) (1942), 535-537.
  7. M. Abtahi, Common fixed point theorems of Meir-keeler type in metric spaces, Fixed Point Theory. 1 (2017), 47-56.
  8. H. Nakano, Modular Semi-Ordered Spaces, Maruzen Co. Ltd., Tokyo, Japan, 1950.
  9. J. Musielak, W. Orlicz, On modular spaces, Stud. Math. 18 (1) (1959) 49-65.
  10. P. Kumam, Fixed point theorems for nonexpansive mappings in modular spaces, Arch. Math. 40 (4) (2004), 345-353.
  11. K. Kuaket, P. Kumam, Fixed points of asymptotic pointwise contractions in modular spaces, Appl. Math. Lett. 24 (11) (2011), 1795-1798.
  12. M. De la Sen, D. O'Regan, R. Saadati, Characterization of modular spaces, J. Comput. Anal. Appl. 22 (2017), 558-572.
  13. K. Fallahi, K. Nourouzi, Probabilistic modular spaces and linear operators, Acta Appl. Math. 105 (2) (2009), 123-140.
  14. A. N. Sherstnev, On the notion of a random normed space, Dokl. Akad. Nauk SSSR. 149 (1963), 280-283.
  15. F. Lael, K. Nourouzi, Fixed points of mappings defined on probabilistic modular spaces, Bull. Math. Anal. Appl. 4 (3) (2012), 23-28.
  16. X. Wang, C. Zhang, Y. Cui, Some sufficient conditions for points of multivalued nonexpansive mappings in banach spaces, Math. Inequal. Appl. 11 (1) (2017), 113-120.