Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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FIXED POINT THEOREMS OF EXTENSION AND MODIFIED EXTENSION α-F-CONTRACTION ON COMPLETE METRIC SPACE

  • Saeed A. A. Al-Salehi (School of Mathematics at Science College, Swami Ramanand Teerth Marathwada University) ;
  • V. C. Borkar (School of Mathematics at Yeshwant Mahavidyalaya College, Swami Ramanand Teerth Marathwada University)
  • Received : 2023.08.14
  • Accepted : 2024.03.22
  • Published : 2024.06.15
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Abstract

The concept of an extension α-F-contraction and it's modified counterpart represents an advancement in the theory of metric space contractions. Through our study of the contraction principles and it's relationship to extension and modified extension, we found different conditions somewhat lengthy. In our paper, we create a development of the conditions for the extension of α-F-contraction and a modified α-F-contraction by reducing the conditions and make them easier. Our propose conditions are notably simple and effective. They serve as the foundation for proving theorems and solving examples that belong to our study. Moreover, they have remarkable significance in the condition of mathematical analysis and problem-solving. Thus, we find that these new conditions that we mention in the definitions achieve what is require and through them, we choose λ = 1 and we choose λ ∈ (0, 1) to clarify our ideas.

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Acknowledgement

We thank the referees for their time and comments

References

  1. S.A. Al-Salehi and V. Borkar, Fixed Points on One Type of F-Weak Contraction in Complete Metric Spaces, Novyi Mir Research Journal, 7(5) (2022), 80-87.
  2. M. Anwar, D. Shehwar, R. Ali and N. Hussain, Wardowski Type α-F-Contractive Approach for Nonself Multivalued Mappings, UPB Sci. Bull. Ser. A, 82 (2020), 69-77.
  3. S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux S. equations integrales, Fund. Math., 3 (1922), 133-181.
  4. L.B. Ciric, A generalization of banachs contraction principl, Proc. Amer. Math. Soc., 45 (1974), 267-273.
  5. P. Das and L.K. Dey, A fixed point theorem in a generalized metric space, Soochow J. Math., 33(1) (2007), 33-39.
  6. P. Das and L.K. Dey, Fixed point of contractive mappings in generalized metric spaces, Math. Slovaca, 59 (2009), 499-504.
  7. L.K. Dey, P. Kumam and T. Senapati, Fixed point results concerning α-F-contraction mappings in metric spaces, Appl. General Topology, 20(1) (2019), 81-95.
  8. L.K. Dey and S. Mondal, Best proximity point of F-contraction in complete metric space, Bull. Allahabad Math. Soc., 30(2) (2015), 173-189.
  9. N.V. Dung and V.T L. Hang, A fixed point theorem for generalized F-contractions on complete metric spaces, Vietnam J. Math., 43(4) (2015), 743-753.
  10. M. Edelstein, An extension of banachs contraction principle, Rev. Anal. Numer. Theor. Approx., 12(1) (1961), 7-10.
  11. M. Farhan, U. Ishtiaq, M. Saeed, A. Hussain and H, Al Sulami, Reich-Type and (α-F)-Contractions in Partially Ordered Double-Controlled Metric-Type Spaces with Applications to Non-Linear Fractional Differential Equations and Monotonic Iterative Method, Axioms, 11(10) (2022), 573.
  12. N. Fabiano, Z. Kadelburg, N. Mirkov Vesna Sesum Cavic and S. Radenovic, On F-Contractions: A Survey, Contemporary Math.,3(3) (2022), 270-385.
  13. A. Fulga and A. Proca, A new Generalization of Wardowski Fixed Point theorem in Complete Metric Spaces, Adv. Theory Nonlinear Anal. Appl., 1(1) (2017), 57-63.
  14. D. Gopal, M. Abbas, D.K. Patel and C. Vetro, Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation, Acta Math. Sci., 36B(3) (2016), 1-14.
  15. N. Hussain and P. Salimi Salimi, Suzuki-Wardowski type fixed point theorems for α-GF-contractions, Taiwanese J. Math., 18(6) (2014), 1879-1895.
  16. E. Karapnar, P. Kumam and P. Salimi, On α-ψ-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013(94) (2013).
  17. G. S. Saluja, H. G. Hyun and J. K. Kim, Generalized integral type F-contraction in partial metric spaces and common fixed points, Nonlinear Funct. Anal. Appl., 28(1) (2023), 107-121.
  18. B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal., 75 (2012) 2154-2165.
  19. N.A. Secelean, Weak F-contractions and some fixed point results, Bulletin Iranian Math. Soc., 42(3), (2016), 779-798
  20. N. Secelean and D. Wardowski, ψ-F-contractions: not necessarily non-expansive Picard operators, Results in Math., 70(3-4) (2016), 415-431.
  21. T. Senapati, L.K. Dey and D. D. Deki'c, Extensions of Ciric and Wardowski type fixed point theorems in D-generalized metric spaces, Fixed Point Theory Appl., 2016(3) (2016).
  22. S. Shukla, D. Gopal and J. Martnez-Moreno, Fixed points of set-valued F-contractions and its application to non-linear integral equations, Filomat, 31(11) (2017), 3377-3390.
  23. T. Stephen, Y. Rohen, M. K. Singh and K. S. Devi, Some rational F-contractions in b-metric spaces and fixed points, Nonlinear Funct. Anal. Appl., 27(2) (2022), 309-322.
  24. D. Wardowski, Fixed points of new type of contractive mappings in complete metric space Fixed Point Theory Appl., 2012, 2012: 94.