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A common fixed point theorem for multi-valued θ_{δ} contractions via subsequential continuity

Year 2020, Volume: 69 Issue: 2, 1473 - 1483, 31.12.2020
https://doi.org/10.31801/cfsuasmas.748142

Abstract

The main objective of this paper is to present a common fixed
point theorem for two pairs of single and set valued mappings via subsequential
continuity and \delta- compatibility. To illustrate the validity of our results, an
example is provided and we give also an application for a system of integral
inclusions of Volterra type.

Thanks

We would like to thanks the editor and any one who will review this manuscript.

References

  • Acar, O., A Fixed Point Theorem for multivalued almost F_{δ}-contraction, Results Math., 72(3) (2017), 1545-1553.
  • Beloul, S., Common fixed point theorems for weakly subsequentially continuous generalized contractions with applications, Appl. Maths. E-Notes, 15 (2015), 173-186.
  • Beloul, S., Chauhan, S., Gregus type fixed points for weakly subsequentially continuous mappings satisfying strict contractive condition of integral type, Le Mathematiche, 71(2) (2017), 3-15.
  • Beloul, S., Common Fixed Point Theorem for strongly tangential and weakly Compatible mappings satisfying implicit relations, Thai. J. Math., 15(2) (2017), 349-358.
  • Beloul, S., Tomar, A., A coincidence and common fixed point theorem for subsequentially continuous hybrid pairs of maps satisfying an implicit relation, Math. Moravica, 21(2) (2017), 15-25.
  • Beloul, S., Kaddouri, H., Fixed Point Theorems For Subsequentially Multi-Valued F_{δ}-Contractions In Metric Spaces, Facta Univ Nis Ser. Math. Inform., 35(2) (2020), 379-392.
  • Bouhadjera, H., Godet Thobie, C., Common fixed point theorems for pairs of subcompatible maps, .(2009), arXiv:0906.3159v1 [math.FA].
  • Ćirić, L. B., Generalization of Banach's Contraction Principle, Proc. Amer. Math. Soc., 45 (1974), 267-273.
  • Durmaz, G., Some theorems for a new type of multivalued contractive maps on metric space, Turkish J. Math., 41, (2017), 1092-1100.
  • Fisher, B., Fixed points for set-valued mappings on metric spaces, Bull. Malays. Math. Sci. Soc., 2(4) (1981), 95-99.
  • Isik. H, Ionescu, C., New type of multivalued contractions with related results and applications, U.P.B. Sci. Bull., Series A, 80(2) (2018), 13-22.
  • Jleli. M, Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014:38, (2014), 8 pp.
  • Jungck, G., Commuting mappings and fixed points, Amer. Math. Monthly, 83(4) (1976), 261-263.
  • Jungck, G., Compatible mappings and common fixed points, Int.J.Math.and Math. Sci., 9(4) (1986), 771-779.
  • Jungck, G., Rhoades, B.E.,Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory, 9 (2008), 383-384.
  • Kaneko, H., Sessa, S., Fixed point theorems for compatible multi-valued and single-valued mappings, Internat. J. Math. Math. Sci., 12(2) (1989), 257-262.
  • Liu, C., Li-Shan, Common fixed points of a pair of single valued mappings and a pair of set valued mappings, Qufu Shifan Daxue Xuebao Ziran Kexue Ban, 18 (1992), 6-10.
  • Nadler, S. B., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488.
  • Pant, R. P., A common fixed point theorem under a new condition, Indian J. Pure Appl. Math. 30(2) (1999), 147-152.
  • Sessa, S., On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. Beograd, 32(46) (1982), 149-153.
  • Singh, S. L., Mishra, S. N., Coincidence and fixed points of reciprocally continuous and compatible hybrid maps, Internat. J. Math. Math. Sci., 10 (2002), 627-635.
Year 2020, Volume: 69 Issue: 2, 1473 - 1483, 31.12.2020
https://doi.org/10.31801/cfsuasmas.748142

Abstract

References

  • Acar, O., A Fixed Point Theorem for multivalued almost F_{δ}-contraction, Results Math., 72(3) (2017), 1545-1553.
  • Beloul, S., Common fixed point theorems for weakly subsequentially continuous generalized contractions with applications, Appl. Maths. E-Notes, 15 (2015), 173-186.
  • Beloul, S., Chauhan, S., Gregus type fixed points for weakly subsequentially continuous mappings satisfying strict contractive condition of integral type, Le Mathematiche, 71(2) (2017), 3-15.
  • Beloul, S., Common Fixed Point Theorem for strongly tangential and weakly Compatible mappings satisfying implicit relations, Thai. J. Math., 15(2) (2017), 349-358.
  • Beloul, S., Tomar, A., A coincidence and common fixed point theorem for subsequentially continuous hybrid pairs of maps satisfying an implicit relation, Math. Moravica, 21(2) (2017), 15-25.
  • Beloul, S., Kaddouri, H., Fixed Point Theorems For Subsequentially Multi-Valued F_{δ}-Contractions In Metric Spaces, Facta Univ Nis Ser. Math. Inform., 35(2) (2020), 379-392.
  • Bouhadjera, H., Godet Thobie, C., Common fixed point theorems for pairs of subcompatible maps, .(2009), arXiv:0906.3159v1 [math.FA].
  • Ćirić, L. B., Generalization of Banach's Contraction Principle, Proc. Amer. Math. Soc., 45 (1974), 267-273.
  • Durmaz, G., Some theorems for a new type of multivalued contractive maps on metric space, Turkish J. Math., 41, (2017), 1092-1100.
  • Fisher, B., Fixed points for set-valued mappings on metric spaces, Bull. Malays. Math. Sci. Soc., 2(4) (1981), 95-99.
  • Isik. H, Ionescu, C., New type of multivalued contractions with related results and applications, U.P.B. Sci. Bull., Series A, 80(2) (2018), 13-22.
  • Jleli. M, Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014:38, (2014), 8 pp.
  • Jungck, G., Commuting mappings and fixed points, Amer. Math. Monthly, 83(4) (1976), 261-263.
  • Jungck, G., Compatible mappings and common fixed points, Int.J.Math.and Math. Sci., 9(4) (1986), 771-779.
  • Jungck, G., Rhoades, B.E.,Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory, 9 (2008), 383-384.
  • Kaneko, H., Sessa, S., Fixed point theorems for compatible multi-valued and single-valued mappings, Internat. J. Math. Math. Sci., 12(2) (1989), 257-262.
  • Liu, C., Li-Shan, Common fixed points of a pair of single valued mappings and a pair of set valued mappings, Qufu Shifan Daxue Xuebao Ziran Kexue Ban, 18 (1992), 6-10.
  • Nadler, S. B., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488.
  • Pant, R. P., A common fixed point theorem under a new condition, Indian J. Pure Appl. Math. 30(2) (1999), 147-152.
  • Sessa, S., On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. Beograd, 32(46) (1982), 149-153.
  • Singh, S. L., Mishra, S. N., Coincidence and fixed points of reciprocally continuous and compatible hybrid maps, Internat. J. Math. Math. Sci., 10 (2002), 627-635.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Ali Ahmed

Saadia Mahideb This is me 0000-0001-6207-2710

Said Beloul 0000-0002-2814-2161

Publication Date December 31, 2020
Submission Date June 4, 2020
Acceptance Date October 10, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Ahmed, A., Mahideb, S., & Beloul, S. (2020). A common fixed point theorem for multi-valued θ_{δ} contractions via subsequential continuity. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1473-1483. https://doi.org/10.31801/cfsuasmas.748142
AMA Ahmed A, Mahideb S, Beloul S. A common fixed point theorem for multi-valued θ_{δ} contractions via subsequential continuity. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1473-1483. doi:10.31801/cfsuasmas.748142
Chicago Ahmed, Ali, Saadia Mahideb, and Said Beloul. “A Common Fixed Point Theorem for Multi-Valued θ_{δ} Contractions via Subsequential Continuity”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1473-83. https://doi.org/10.31801/cfsuasmas.748142.
EndNote Ahmed A, Mahideb S, Beloul S (December 1, 2020) A common fixed point theorem for multi-valued θ_{δ} contractions via subsequential continuity. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1473–1483.
IEEE A. Ahmed, S. Mahideb, and S. Beloul, “A common fixed point theorem for multi-valued θ_{δ} contractions via subsequential continuity”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1473–1483, 2020, doi: 10.31801/cfsuasmas.748142.
ISNAD Ahmed, Ali et al. “A Common Fixed Point Theorem for Multi-Valued θ_{δ} Contractions via Subsequential Continuity”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1473-1483. https://doi.org/10.31801/cfsuasmas.748142.
JAMA Ahmed A, Mahideb S, Beloul S. A common fixed point theorem for multi-valued θ_{δ} contractions via subsequential continuity. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1473–1483.
MLA Ahmed, Ali et al. “A Common Fixed Point Theorem for Multi-Valued θ_{δ} Contractions via Subsequential Continuity”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1473-8, doi:10.31801/cfsuasmas.748142.
Vancouver Ahmed A, Mahideb S, Beloul S. A common fixed point theorem for multi-valued θ_{δ} contractions via subsequential continuity. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1473-8.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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