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A fixed point theorem for mappings with an F-contractive iterate

Year 2019, Volume: 3 Issue: 4, 231 - 236, 30.12.2019
https://doi.org/10.31197/atnaa.644325

Abstract

In this paper, we introduce the notion of $F$-contraction in the setting of complete metric space and we prove a fixed point theorem for $F$-contractive iteration.

References

  • M. Abbas, M. Berzig, T. Nazir, E. Karapinar, Iterative Approximation of Fixed Points for Presic Type F-Contraction Operators,University Politehnica Of Bucharest Scientific Bulletin-Series A-Applied Mathematics And Physics, 78(2) (2016), 147-160.
  • B. Alqahtani, A. Fulga, E. Karapinar, A fixed point result with a contractive iterate at a point, Mathematics, 7(7) (2019), 606.
  • B. Alqahtani, A. Fulga, E. Karapinar, P. S. Kumari, Sehgal Type Contractions on Dislocated Spaces, Mathematics, 7(2) (2019), 153.
  • B. Alqahtani, A. Fulga, E. Karapınar, Sehgal Type Contractions on b-Metric Space, Symmetry, 10 (2018), 560.
  • H. H. Alsulami, E. Karapinar, H. Piri, Fixed Points of Modified F-Contractive Mappings in Complete Metric-Like Spaces, Journal of Function Spaces, 2015 (2015), Article ID 270971, 9 pages.
  • H.H. Alsulami, E. Karapınar, F. Khojasteh, A.F. Roldán-López-de-Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dynamics in Nature and Society, Article ID 269286, (2014), 10 pages
  • H. Aydi, E. Karapinar, H. Yazidi, Modified F-Contractions via alpha-Admissible Mappings and Application to Integral Equations, Filomat, 31(5) (2017), 1141- 148. S.
  • Banach, Sur les op\'{e}rations dans les ensembles abstraits et leur application aux \'{e}quations int\'{e}grales, Fundamenta Mathematicae, 3 (1922), 133--181.
  • M. Bota, Fixed point theorems for operators with a contractive iterate in $b$-metric spaces, Stud. Univ. Babes-Bolyai Math. 61(2016), No. 4, 435--442.
  • V. W. Bryant, A remark on a fixed point theorem for iterated mappings, The American Mathematical Monthly, vol. 75, pp. 399--400, 1968.
  • Lj. B. \'{C}iri\'{c}, On Sehgal's maps with a contractive iterate at a point, Publ. Inst. Math. (Beograd) (N.S.), 33 (47) (1983), 59-62.
  • L. F. Guseman, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Am. Math. Soc., 26 (1970), 615-618.
  • E. Karapinar, H. Piri and H.H. AlSulami, Fixed Points of Generalized F-Suzuki Type Contraction in Complete b-Metric Spaces, Discrete Dynamics in Nature and Society, 2015 (2015), Article ID 969726, 8 pages.
  • E. Karapınar, H. Aydi, A. Fulga, W. Shatanavi, Wardowski type contractions with applications on Caputo type nonlinear fractional differential equations, in press
  • F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (6) (2015), 1189-1194
  • Z. D. Mitrovi \'{c}, An Extension of Fixed Point Theorem of Sehgal in $b$-Metric Spaces, Commun. Appl. Nonlinear Anal., 25 (2018), Number 2, 54-61.
  • A.F. Roldán-López-de-Hierro, E. Karapınar, C. Roldán-López-de-Hierro, J. Martínez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math. 275 (2015), 345–355
  • V. M. Sehgal, A fixed point theorem for mappings with a contractive iterate, Proc. Amer. Math. Soc., 23 (1969), 631-634.
  • D. Wardowski: Fixed Points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012).
Year 2019, Volume: 3 Issue: 4, 231 - 236, 30.12.2019
https://doi.org/10.31197/atnaa.644325

Abstract

References

  • M. Abbas, M. Berzig, T. Nazir, E. Karapinar, Iterative Approximation of Fixed Points for Presic Type F-Contraction Operators,University Politehnica Of Bucharest Scientific Bulletin-Series A-Applied Mathematics And Physics, 78(2) (2016), 147-160.
  • B. Alqahtani, A. Fulga, E. Karapinar, A fixed point result with a contractive iterate at a point, Mathematics, 7(7) (2019), 606.
  • B. Alqahtani, A. Fulga, E. Karapinar, P. S. Kumari, Sehgal Type Contractions on Dislocated Spaces, Mathematics, 7(2) (2019), 153.
  • B. Alqahtani, A. Fulga, E. Karapınar, Sehgal Type Contractions on b-Metric Space, Symmetry, 10 (2018), 560.
  • H. H. Alsulami, E. Karapinar, H. Piri, Fixed Points of Modified F-Contractive Mappings in Complete Metric-Like Spaces, Journal of Function Spaces, 2015 (2015), Article ID 270971, 9 pages.
  • H.H. Alsulami, E. Karapınar, F. Khojasteh, A.F. Roldán-López-de-Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dynamics in Nature and Society, Article ID 269286, (2014), 10 pages
  • H. Aydi, E. Karapinar, H. Yazidi, Modified F-Contractions via alpha-Admissible Mappings and Application to Integral Equations, Filomat, 31(5) (2017), 1141- 148. S.
  • Banach, Sur les op\'{e}rations dans les ensembles abstraits et leur application aux \'{e}quations int\'{e}grales, Fundamenta Mathematicae, 3 (1922), 133--181.
  • M. Bota, Fixed point theorems for operators with a contractive iterate in $b$-metric spaces, Stud. Univ. Babes-Bolyai Math. 61(2016), No. 4, 435--442.
  • V. W. Bryant, A remark on a fixed point theorem for iterated mappings, The American Mathematical Monthly, vol. 75, pp. 399--400, 1968.
  • Lj. B. \'{C}iri\'{c}, On Sehgal's maps with a contractive iterate at a point, Publ. Inst. Math. (Beograd) (N.S.), 33 (47) (1983), 59-62.
  • L. F. Guseman, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Am. Math. Soc., 26 (1970), 615-618.
  • E. Karapinar, H. Piri and H.H. AlSulami, Fixed Points of Generalized F-Suzuki Type Contraction in Complete b-Metric Spaces, Discrete Dynamics in Nature and Society, 2015 (2015), Article ID 969726, 8 pages.
  • E. Karapınar, H. Aydi, A. Fulga, W. Shatanavi, Wardowski type contractions with applications on Caputo type nonlinear fractional differential equations, in press
  • F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (6) (2015), 1189-1194
  • Z. D. Mitrovi \'{c}, An Extension of Fixed Point Theorem of Sehgal in $b$-Metric Spaces, Commun. Appl. Nonlinear Anal., 25 (2018), Number 2, 54-61.
  • A.F. Roldán-López-de-Hierro, E. Karapınar, C. Roldán-López-de-Hierro, J. Martínez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math. 275 (2015), 345–355
  • V. M. Sehgal, A fixed point theorem for mappings with a contractive iterate, Proc. Amer. Math. Soc., 23 (1969), 631-634.
  • D. Wardowski: Fixed Points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012).
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ali Öztürk 0000-0001-6014-9112

Publication Date December 30, 2019
Published in Issue Year 2019 Volume: 3 Issue: 4

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