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Fixed point results for decreasing convex orbital operators in Hilbert spaces

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Abstract

Let \((X, \left\langle \cdot \right\rangle )\) be a Hilbert space and \(T:X\rightarrow X\) be a decreasing operator. Under a metric condition involving the convex combination of x and T(x), we will prove some fixed point theorems which generalize and complement several results in the theory of nonlinear operators. Our results are closely related to the admissible perturbations approach in fixed point theory.

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References

  1. Alghamdi, M.A., Alnafei, S.H., Radenović, S., Shahzad, N.: Fixed point theorems for convex contraction mappings on cone metric spaces. Math. Comput. Model. 54, 2020–2026 (2011)

    Article  MathSciNet  Google Scholar 

  2. Berinde, V., Păcurar, M.: Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22, 38 (2020)

    Article  MathSciNet  Google Scholar 

  3. Berinde, V.: Approximating fixed points of almost convex contractions in metric spaces. Ann. Acad. Rom. Sci. Ser. Math. Appl. 12, 11–23 (2020)

    MathSciNet  MATH  Google Scholar 

  4. Berinde, V., Petruşel, A., Rus, I.A., Şerban, M.A.: The retraction-displacement condition in the theory of fixed point equation with a convergent iterative algorithm. In: Rassias, T., Gupta, V. (eds.) Mathematical Analysis, Approximation Theory and Their Applications, pp. 75–106. Springer, Cham (2016)

    Chapter  Google Scholar 

  5. Berinde, V.: Convergence theorems for fixed point iterative methods defined as admissible perturbations of a nonlinear operator. Carpathian J. Math. 29, 9–18 (2013)

    Article  MathSciNet  Google Scholar 

  6. Bisht, R.K., Hussain, N.: A note on convex contraction mappings and discontinuity at fixed point. J. Math. Anal. 8, 90–96 (2017)

    MathSciNet  Google Scholar 

  7. Ćirić, Lj.B.: A generalization of Banach’s contraction principle. Proc. Am. Math. Soc. 45, 267–273 (1974)

  8. Istrăţescu, V.I.: Some fixed point theorems for convex contraction mappings and convex nonexpansive mappings. I. Lib. Math. 1, 151–163 (1981)

    MathSciNet  MATH  Google Scholar 

  9. Kirk, W.A., Sims, B. (eds.): Handbook of Metric Fixed Point Theory. Kluwer Academic Publishers, Dordrecht (2001)

    MATH  Google Scholar 

  10. Latif, A., Sintunavarat, W., Ninsri, A.: Approximate fixed point theorems for partial generalized convex contraction mappings in \(\alpha \)-complete metric spaces. Taiwan. J. Math. 19, 315–333 (2015)

    Article  MathSciNet  Google Scholar 

  11. Miandaragh, M.A., Postolache, M., Rezapour, S.: Approximate fixed points of generalized convex contractions. Fixed Point Theory Appl 2013, 255 (2013)

    Article  MathSciNet  Google Scholar 

  12. Ostrowski, A.M.: The round off stability of iterations. Z. Angew. Math. Mech. 47, 77–81 (1967)

    Article  MathSciNet  Google Scholar 

  13. Petruşel, A., Rus, I.A.: Graphic contraction principle and applications. In: Rassias, T.M., Pardalos, P.M. (eds.) Mathematical Analysis and Applications, pp. 411–432. Springer, Cham (2019)

    Chapter  Google Scholar 

  14. Reich, S.: Some remarks concerning contractions mappings. Can. Math. Bull. 14, 121–124 (1971)

    Article  MathSciNet  Google Scholar 

  15. Reich, S.: Fixed point of contractive functions. Boll. Un. Mat. Ital. 5, 26–42 (1972)

    MathSciNet  MATH  Google Scholar 

  16. Reich, S., Zaslavski, A.J.: Well-posedness of fixed point problems. Far East J. Math. Sci. Special Volume (Functional Analysis and its Applications), Part III, 393–401 (2001)

  17. Reich, S., Zaslavski, A.J.: Genericity in Nonlinear Analysis. Springer, New York (2014)

    Book  Google Scholar 

  18. Rus, I.A.: Some variants of contraction principle, generalizations and applications. Stud. Univ. Babeş-Bolyai Math. 61, 343–358 (2016)

    MathSciNet  MATH  Google Scholar 

  19. Rus, I.A.: Results and problems in Ulam stability of operatorial equations and inclusions. In: Rassias, T. (ed.) Handbook of Functional Equations. Springer Optimization and Its Applications, vol. 96, pp. 323–352. Springer, New York (2014)

    Chapter  Google Scholar 

  20. Rus, I.A., Şerban, M.-A.: Basic problems of the metric fixed point theory and the relevance of a metric fixed point theorem. Carpathian J. Math. 29, 239–258 (2013)

    Article  MathSciNet  Google Scholar 

  21. Rus, I.A.: An abstract point of view on iterative approximation of fixed point equations. Fixed Point Theory 13, 179–192 (2012)

    MathSciNet  MATH  Google Scholar 

  22. Rus, I.A.: Properties of the solutions of those equations for which the Krasnoselskii iteration converges. Carpathian J. Math. 28, 329–336 (2012)

    Article  MathSciNet  Google Scholar 

  23. Rus, I.A.: Remarks on Ulam stability of the operatorial equations. Fixed Point Theory 10, 305–320 (2009)

    MathSciNet  MATH  Google Scholar 

  24. Rus, I.A., Petruşel, A., Petruşel, G.: Fixed Point Theory. Cluj University Press, Cluj-Napoca (2008)

    MATH  Google Scholar 

  25. Tongnoi, B.: Saturated versions of some fixed point theorems for generalized contractions. Fixed Point Theory 21, 755–766 (2020)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Adrian Petruşel

  2. Department of Business, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Gabriela Petruşel

Authors
  1. Adrian Petruşel
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  2. Gabriela Petruşel
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Correspondence to Adrian Petruşel.

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Petruşel, A., Petruşel, G. Fixed point results for decreasing convex orbital operators in Hilbert spaces. J. Fixed Point Theory Appl. 23, 35 (2021). https://doi.org/10.1007/s11784-021-00873-1

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