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Year 2020, Volume: 3 Issue: 1, 160 - 165, 15.12.2020

Nihal Taş

Abstract

References

  • 1 S. Banach, Sur les operations dans les ensembles abstrait et leur application aux equations integrals, Fundam. Math. 3 (1922), 133-181.
  • 2 R.K. Bisht, R. P. Pant, A remark on discontinuity at fixed point, J. Math. Anal. Appl. 445(2) (2017) 1239-1242.
  • 3 J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Am. Math. Soc. 215 (1976), 241-251.
  • 4 U. Çelik, N. Özgür, A new solution to the discontinuity problem on metric spaces, Turk. J. Math. 44 (2020), 1115-1126.
  • 5 Lj. B. Ciric, A generalization of Banach’s contraction principle, Proc. Am. Math. Soc. 45(2) (1974), 267-273.
  • 6 L. J. Cromme, I. Diener, Fixed point theorems for discontinuous mapping, Math. Program. 51(1-3) (1991), 257-267.
  • 7 T. Dosenovic, S. Radenovic, S. Sedghi, Generalized metric spaces: survey, TWMS J. Pure Appl. Math. 9(1) (2018), 3-17.
  • 8 E. Karapınar, F. Khojasteh, W. Shatanawia, Revisiting Ciric-Type Contraction with Caristi’s Approach, Symmetry 11 (2019), 726.
  • 9 F. Khojasteh, S. Shukla, S. Radenovi´c, A new approach to the study of fixed point theory for simulation functions, Filomat 29(6) (2015), 1189-1194.
  • 10 A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326-329.
  • 11 N. Y. Özgür, N. Ta¸s, Some fixed-circle theorems and discontinuity at fixed circle, AIP Conference Proceedings 1926 (2018), 020048.
  • 12 N. Y. Özgür, N. Ta¸s, Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc. 42(4) (2019), 1433-1449.
  • 13 N. Y. Özgür, Fixed-disc results via simulation functions, Turk. J. Math. 43(6) (2019), 2794-2805.
  • 14 R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl. 240(1) (1999), 284-289.
  • 15 A. Pant, R. P. Pant, Fixed points and continuity of contractive maps, Filomat 31(11) (2017), 3501-3506.
  • 16 R. P. Pant, N. Y. Özgür, N. Ta¸s, Discontinuity at fixed points with applications, Bull. Belg. Math. Soc. - Simon Stevin 26 (2019), 571-589.
  • 17 R. P. Pant, N. Y. Özgür, N. Ta¸s, On discontinuity problem at fixed point, Bull. Malays. Math. Sci. Soc. 43(1) (2020), 499-517.
  • 18 M. Rashid, I. Batool, N. Mehmood, Discontinuous mappings at their fixed points and common fixed points with applications, J. Math. Anal. 9(1) (2018), 90-104.
  • 19 B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Am. Math. Soc. 226 (1977), 257-290.
  • 20 B. E. Rhoades, Contractive definitions and continuity, Contemp. Math. 72 (1988), 233-245.
  • 21 N. Ta¸s, N. Y. Özgür, A new contribution to discontinuity at fixed point, Fixed Point Theory 20(2) (2019), 715-728.
  • 22 N. Ta¸s, N. Y. Özgür, N. Mlaiki, New types of FC-contractions and the fixed-circle problem, Mathematics 6(10) (2018), 188.
  • 23 N. Ta¸s, Bilateral-type solutions to the fixed-circle problem with rectified linear units application, Turk. J. Math. 44 (2020), 1330-1344.
  • 24 M. J. Todd, The computation of fixed points and applications, Berlin, Heidelberg, New York: Springer-Verlag, 1976.
  • 25 D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), 94.

New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem

Year 2020, Volume: 3 Issue: 1, 160 - 165, 15.12.2020

Nihal Taş

Abstract

Recently, the Rhoades' open problem which is related to the discontinuity at fixed point of a self-mapping and the fixed-circle problem which is related to the geometric meaning of the set of fixed points of a self-mapping have been studied using various approaches. Therefore, in this paper, we give some solutions to the Rhoades' open problem and the fixed-circle problem on metric spaces. To do this, we inspire from the
Meir-Keeler type, Ciric type and Caristi type fixed-point theorems. Also, we use the simulation functions and Wardowski's technique to obtain new fixed-circle results.

Keywords

Fixec circle Fixed disc Fixed point Metric space

References

  • 1 S. Banach, Sur les operations dans les ensembles abstrait et leur application aux equations integrals, Fundam. Math. 3 (1922), 133-181.
  • 2 R.K. Bisht, R. P. Pant, A remark on discontinuity at fixed point, J. Math. Anal. Appl. 445(2) (2017) 1239-1242.
  • 3 J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Am. Math. Soc. 215 (1976), 241-251.
  • 4 U. Çelik, N. Özgür, A new solution to the discontinuity problem on metric spaces, Turk. J. Math. 44 (2020), 1115-1126.
  • 5 Lj. B. Ciric, A generalization of Banach’s contraction principle, Proc. Am. Math. Soc. 45(2) (1974), 267-273.
  • 6 L. J. Cromme, I. Diener, Fixed point theorems for discontinuous mapping, Math. Program. 51(1-3) (1991), 257-267.
  • 7 T. Dosenovic, S. Radenovic, S. Sedghi, Generalized metric spaces: survey, TWMS J. Pure Appl. Math. 9(1) (2018), 3-17.
  • 8 E. Karapınar, F. Khojasteh, W. Shatanawia, Revisiting Ciric-Type Contraction with Caristi’s Approach, Symmetry 11 (2019), 726.
  • 9 F. Khojasteh, S. Shukla, S. Radenovi´c, A new approach to the study of fixed point theory for simulation functions, Filomat 29(6) (2015), 1189-1194.
  • 10 A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326-329.
  • 11 N. Y. Özgür, N. Ta¸s, Some fixed-circle theorems and discontinuity at fixed circle, AIP Conference Proceedings 1926 (2018), 020048.
  • 12 N. Y. Özgür, N. Ta¸s, Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc. 42(4) (2019), 1433-1449.
  • 13 N. Y. Özgür, Fixed-disc results via simulation functions, Turk. J. Math. 43(6) (2019), 2794-2805.
  • 14 R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl. 240(1) (1999), 284-289.
  • 15 A. Pant, R. P. Pant, Fixed points and continuity of contractive maps, Filomat 31(11) (2017), 3501-3506.
  • 16 R. P. Pant, N. Y. Özgür, N. Ta¸s, Discontinuity at fixed points with applications, Bull. Belg. Math. Soc. - Simon Stevin 26 (2019), 571-589.
  • 17 R. P. Pant, N. Y. Özgür, N. Ta¸s, On discontinuity problem at fixed point, Bull. Malays. Math. Sci. Soc. 43(1) (2020), 499-517.
  • 18 M. Rashid, I. Batool, N. Mehmood, Discontinuous mappings at their fixed points and common fixed points with applications, J. Math. Anal. 9(1) (2018), 90-104.
  • 19 B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Am. Math. Soc. 226 (1977), 257-290.
  • 20 B. E. Rhoades, Contractive definitions and continuity, Contemp. Math. 72 (1988), 233-245.
  • 21 N. Ta¸s, N. Y. Özgür, A new contribution to discontinuity at fixed point, Fixed Point Theory 20(2) (2019), 715-728.
  • 22 N. Ta¸s, N. Y. Özgür, N. Mlaiki, New types of FC-contractions and the fixed-circle problem, Mathematics 6(10) (2018), 188.
  • 23 N. Ta¸s, Bilateral-type solutions to the fixed-circle problem with rectified linear units application, Turk. J. Math. 44 (2020), 1330-1344.
  • 24 M. J. Todd, The computation of fixed points and applications, Berlin, Heidelberg, New York: Springer-Verlag, 1976.
  • 25 D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), 94.
There are 25 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Nihal Taş

Publication Date December 15, 2020
Acceptance Date September 24, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Taş, N. (2020). New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem. Conference Proceedings of Science and Technology, 3(1), 160-165.
AMA Taş N. New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem. Conference Proceedings of Science and Technology. December 2020;3(1):160-165.
Chicago Taş, Nihal. “New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem”. Conference Proceedings of Science and Technology 3, no. 1 (December 2020): 160-65.
EndNote Taş N (December 1, 2020) New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem. Conference Proceedings of Science and Technology 3 1 160–165.
IEEE N. Taş, “New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 160–165, 2020.
ISNAD Taş, Nihal. “New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem”. Conference Proceedings of Science and Technology 3/1 (December 2020), 160-165.
JAMA Taş N. New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem. Conference Proceedings of Science and Technology. 2020;3:160–165.
MLA Taş, Nihal. “New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem”. Conference Proceedings of Science and Technology, vol. 3, no. 1, 2020, pp. 160-5.
Vancouver Taş N. New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem. Conference Proceedings of Science and Technology. 2020;3(1):160-5.
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