Ufuk Çelik, Nihal Özgür

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In this paper, we obtain new fixed point results with the help of various techniques constructed by using auxiliary numbers and some family of functions. In the context of the fixed-circle (resp. fixed-disc) problem, we consider the geometry of the fixed point set of a self-mapping on a metric space. Also, we discuss the effectiveness of our theoretical fixed point results by considering possible applications to the study of neural networks.


Fixed circle, fixed disc, implicit relation

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H. Ahmad, M. Younis and M. E. Koksal: Double controlled partial metric type spaces and convergence results. J. Math. 2021 (2021), Art. ID 7008737, 11 pp.

I Altun and D. Turkoglu: Some fixed point theorems for weakly compatible mappings satisfying an implicit relation. Taiwanese J. Math. 13 (2009), 1291–1304.

T. V. An, N. V. Dung and V. T. L. Hang: General fixed point theorems on metric spaces and 2-metric spaces. Filomat 28 (2014), 2037–2045.

H. Aydi, N. Tas, N. Ozgur and N. Mlaiki: Fixed-discs in rectangular metric spaces. Symmetry 11 (2019), 294.

R. K. Bisht and N. Ozgur: Discontinuous convex contractions and their applications in neural networks. Comput. Appl. Math. 40 (2021), Paper No. 11, 11 pp.

S. H. Chang: Existence-uniqueness and fixed-point iterative method for general nonlinear fourth-order boundary value problems. J. Appl. Math. Comput. 67 (2021), 221–231.

U. Celik: Geometry of fixed points and discontinuity at fixed points. Ph. D. Thesis, Balıkesir University, Balıkesir, 2021.

U. Celik and N. Ozgur: A new solution to the discontinuity problem on metric spaces. Turkish J. Math 44 (2020), 1115–1126.

U. Celik and N. Ozgur: On the fixed-circle problem. Facta Univ. Ser. Math. Inform. 35 (2020), 1273–1290.

K. Ezzinbi and M. A. Taoudi: Sadovskii-Krasnosel’skii type fixed point theorems in Banach spaces with application to evolution equations. J. Appl. Math. Comput. 49 (2015), 243–260.

Y. J. Huang, S. J. Chen, X. H. Yang and J. Xiao: Coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions. Chinese Physics B 28 (2019), 040701.

M. Imdad, S. Kumar and M. S. Khan: Remarks on some fixed point theorems satisfying implicit relations. Dedicated to the memory of Prof. Dr. Naza Tanovic-Miller. Rad. Mat. 11 (2002), 1–9.

L. K. Li: Fixed point analysis for discrete-time recurrent neural networks. In: [Proceedings 1992] IJCNN International Joint Conference on Neural Networks, IEEE, Vol. 4, 1992, 134–139.

N. Mlaiki, U. C¸ elik, N. Tas¸, N. ¨Ozg¨ur and A. Mukheimer: Wardowski type contractions and the fixed-circle problem on S-metric spaces. J. Math. 2018 (2018), Art. ID 9127486, 9 pp.

N. Mlaiki, N. Tas and N. Ozgur: On the fixed-circle problem and Khan type contractions. Axioms 7 (2018), 80.

N. Mlaiki, N. Ozgur and N. Tas¸: New fixed-circle results related to Fccontractive and Fc-expanding mappings on metric space. (2021). Available from:

X. Nie and W. X. Zheng: On Stability of Multiple Equilibria for Delayed Neural Networks with Discontinuous activation Functions. In:Proceeding of the 34th Chinese Control Conference July 28-30, 2015.

X. Nie and W. X. Zheng: Complete stability of neural networks with nonmonotonic piecewise linear activation functions. IEEE Transactions on Circuits and Systems II: Express Briefs 62 (2015), 1002–1006.

X. Nie, J. Cao and S. Fei: Multistability and instability of competitive neural networks with non-monotonic piecewise linear activation functions. Nonlinear Anal., Real World Appl. 45 (2019), 799–821.

N. Ozgur: Fixed-disc results via simulation functions. Turkish J. Math. 43 (2019), 2794–2805.

N. Ozgur and N. Tas: Some fixed-circle theorems and discontinuity at fixed circle. In: AIP Conference Proceedings, AIP Publishing LLC 1926 (2018), 020048.

N. Y. Ozgur, N. Tas and U. Celik: New fixed-circle results on S-metric spaces. Bull. Math. Anal. Appl. 9 (2017), 10–23.

N. Tas and N. Ozgur: A new contribution to discontinuity at fixed point. Fixed Point Theory 20 (2019), 715–728.

A. Tomar, J. Meena and S. K. Padaliya: Fixed point to fixed circle and activation function in partial metric space. J. Appl. Anal. 28 (2022), 57–66.

N. Y. Ozgur and N. Tas: Fixed-circle problem on S-metric spaces with a geometric viewpoint. Facta Univ. Ser. Math. Inform. 34 (2019), 459–472.

N. Y. Ozgur and N. Tas: Some fixed-circle theorems on metric spaces. Bull. Malays. Math. Sci. Soc. 42 (2019), 1433–1449.

R. P. Pant, N. Y. Ozgur and N. Tas: On Discontinuity Problem at Fixed Point. Bull. Malays. Math. Sci. Soc. 43 (2020), 499–517.

R. P. Pant, N. Y. Ozgur and N. Tas: Discontinuity at fixed points with applications. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), 571–589.

H. K. Pathak, R. Rodrıguez-Lopez and R. K. Verma: A common fixed point theorem using implicit relation and property (E.A) in metric spaces. Filomat 21 (2007), 211–234.

V. Popa and M. Mocanu: Altering distance and common fixed points under implicit relations. Hacet. J. Math. Stat. 38 (2009), 329–337.

V. Popa: Some fixed point theorems for compatible mappings satisfying an implicit relation. Demonstratio Math. 32 (1999), 157–163.

H. N. Saleh, S. Sessa, W. M. Alfakih, M. Imdad and N. Mlaiki: Fixed circle and fixed disc results for new types of θc−contractive mappings in metric spaces. Symmetry 12 (2020), 1825.

S. Sedghi and N. V. Dung: Fixed point theorems on S-metric spaces. Mat. Vesnik 66 (2014), 113–124.

N. Tas¸, N. Ozgur and N. Mlaiki: New types of Fc−contractions and the fixed-circle problem. Mathematics 6 (2018), 188.

D. Wardowski: Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012 (2012) 94, 6 pp.

M. Younis, D. Singh and A. A. N. Abdou: A fixed point approach for tuning circuit problem in dislocated b-metric spaces. Math. Methods Appl. Sci. 45 (2022), 2234–2253.

M. Younis and D. Singh: On the existence of the solution of Hammerstein integral equations and fractional differential equations. J. Appl. Math. Comput. 68 (2022), 1087–1105.

M. Younis, A. Sretenovic and S. Radenovic: Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractionalorder functional differential equations” . Nonlinear Anal. Model. Control 27 (2022), 163–178.



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