On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces

Mahpeyker ÖZTÜRK, (Sakarya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, Sakarya, Türkiye)
Abdurrahman BÜYÜKKAYA (Karadeniz Teknik Üniversitesi, Fen Fakültesi, Matematik Bölümü, Trabzon, Türkiye)
Fundamental journal of mathematics and applications (Online)
3 1
Yıl: 2022 Cilt: 5 Sayı: 4 Sayfa Aralığı: 210 - 227 Metin Dili: İngilizce DOI: 10.33401/fujma.1107963 İndeks Tarihi: 02-01-2023

On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces

Öz:
This article aims to specify a new $C-$class function endowed with altering distance and ultra altering distance function via generalized $Xi -$contraction, which is called the $mathcal{G}left( {Sigma ,vartheta ,Xi } right) - $contraction in modular $b-$metric spaces. Regarding these new contraction type mappings, the study includes some existence and uniqueness theorems, and to indicate the usability and productivity of these results, some applications related to integral type contractions and an application to the graph structure.
Anahtar Kelime: Common fixed point $C-$class function Modular $b-$metric space

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] S. Banach, Sur les operations dans les emsembles abstraits et leurs applications aux equations integrales, Fund. Math., 1 (1922), 133-181.
  • [2] I. A. Bakhtin, The contraction mapping principle in quasi metric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst., 30 (1989), 26–37.
  • [3] S. Czerwik, Contraction mappings in b􀀀metric spaces, Acta. Math. Inform. Univ. Ostrav, 1 (1) (1993), 5-11.
  • [4] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semin. Mat. Fis. Univ. Modena, 46 (1998), 263-276.
  • [5] A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b􀀀metric spaces, Math. Slovaca, 64 (4) (2014), 941–960.
  • [6] V. V. Chistyakov, Modular metric spaces generated by F-modulars, Folia Math., 15 (2008), 3-24.
  • [7] V. V. Chistyakov, Modular metric spaces, I: Basic concepts. Nonlinear Anal., 72 (2010), 1-14.
  • [8] V. V. Chistyakov, Modular metric spaces, II: Application to superposition operators, Nonlinear Anal., 72 (2010), 15-30.
  • [9] V. V. Chistyakov, Fixed points of modular contractive maps, Dokl. Math., 86 (2012), 515-518.
  • [10] C. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory Appl., 93 (2011), 1-9.
  • [11] M. E. Ege, C. Alaca, Some results for modular b􀀀metric spaces and an application to system of linear equations, Azerbaijan J. Math., 8 (1) (2018), 3-14.
  • [12] V. Parvaneh, N. Hussain, M. Khorshidi, N. Mlaiki, H. Aydi, Fixed point results for generalized F-contractions in modular b-metric spaces with applications, Mathematics, 7 (10) (2019), 1-16.
  • [13] A. H. Ansari, Note on ”j 􀀀y􀀀contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, September/2014, 11 (2014), 377–380.
  • [14] M. S. Khan, M. Swalesh, S. Sessa, Fixed points theorems by altering distances between the points, Bull. Aust. Math. Soc., 30 (1984), 1–9.
  • [15] A. H. Ansari, J. M. Kumar, N. Saleem, Inverse C􀀀class function on weak semi compatibility and fixed point theorems for expansive mappings in G-metric spaces, Math. Morav., 24 (1) (2020), 93-108.
  • [16] A. H. Ansari, T. Dosenovic, S. Radenovic, N. Saleem, V. Sesum-Cavic, C􀀀class functions on some fixed point results in ordered partial metric space via admissible mappings, Novi Sad J. Math., 49 (1) (2019), 101-116. [17] N. Saleem, A. H. Ansari, M. K. Jain, Some fixed point theorems of inverse C􀀀class function under weak semi compatibility, J. Fixed Point Theory, 9 (2018), 2018.
  • [18] A. H. Ansari, N. Saleem, B. Fisher, M. S. Khan, C􀀀class function on Khan type fixed point theorems in generalized metric space, Filomat, 31 (11) (2017), 3483-3494.
  • [19] A. Fulga, A. M. Proca, Fixed point for Geraghty JE􀀀contractions, J. Nonlinear Sci. Appl., 10 (2017), 5125-5131. doi.org/10.22436/jnsa.010.09.48.
  • [20] A. Fulga, A. M. Proca, A new Generalization of Wardowski fixed point theorem in complete metric spaces, Adv. Theory Nonlinear Anal. Appl., 1 (2017), 57-63.
  • [21] A. Fulga, E. Karapınar, Some results on S􀀀contractions of Type E, Mathematics, 195 (6) (2018), 1-9.
  • [22] B. Alqahtani, A. Fulga, E. Karapınar, A short note on the common fixed points of the Geraghty contraction of type ES;T , Demonstr. Math., 51 (2018), 233-240.
  • [23] A. M. Proca, Fixed point theorem for jM􀀀Geraghty contraction, In: Proceedings of the Scientific Research and Education in the Air Force (AFASES2018), May 22-27/2018, Brasov, Romania, 1 (2018), 311-316. doi.org/10.19062/2247-3173.2018.20.41.
  • [24] A. M. Proca, New fixed point theorem for generalized contractions, Bull. Transilv. Univ. Bras. III: Math. Inform. Phys, 12 (61) (2019), 435-442.
  • [25] L. Ciric, On contraction type mappings, Math. Balcanica, 1 (1971), 52-57.
  • [26] G. Jungck, Common fixed points for non-continuous nonself mappings on non-numeric spaces, Far East J. Math. Sci., 4 (2) (1996), 199-212.
  • [27] H. Aydi, A. Felhi, E. Karapınar, S. Sahmim, A Nadler-type fixed point theorem in dislocated spaces and applications, Miskolc. Math. Notes, 19 (2018), 111-124. doi.org/10.18514/mmn.2018.1652.
  • [28] E. Girgin, M. O¨ ztu¨rk, Modified Suzuki-Simulation type contractive mapping in non-Archimedean quasi modular metric spaces and application to graph theory, Mathematics, 7 (9) (2019), 1-14. doi.org/10.3390/math7090769.
  • [29] D. Gopal, C. Vetro, M. Abbas, D. K. Patel, Some coincidence and periodic points results in a metric space endowed with a graph and applications, Banach J. Math. Anal., 9 (2015), 128–140. doi.org/10.15352/bjma/09-3-9.
  • [30] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002), 531-536.
  • [31] B. Azadifar, G. Sadeghi, R. Saadati, C. Park, Integral type contractions in modular metric spaces, J. Inequalities Appl., 483 (2013), 1-14. doi.org/10.1186/1029-242x-2013-483.
APA OZTURK M, Büyükkaya A (2022). On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. , 210 - 227. 10.33401/fujma.1107963
Chicago OZTURK MAHPEYKER,Büyükkaya Abdurrahman On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. (2022): 210 - 227. 10.33401/fujma.1107963
MLA OZTURK MAHPEYKER,Büyükkaya Abdurrahman On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. , 2022, ss.210 - 227. 10.33401/fujma.1107963
AMA OZTURK M,Büyükkaya A On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. . 2022; 210 - 227. 10.33401/fujma.1107963
Vancouver OZTURK M,Büyükkaya A On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. . 2022; 210 - 227. 10.33401/fujma.1107963
IEEE OZTURK M,Büyükkaya A "On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces." , ss.210 - 227, 2022. 10.33401/fujma.1107963
ISNAD OZTURK, MAHPEYKER - Büyükkaya, Abdurrahman. "On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces". (2022), 210-227. https://doi.org/10.33401/fujma.1107963
APA OZTURK M, Büyükkaya A (2022). On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. Fundamental journal of mathematics and applications (Online), 5(4), 210 - 227. 10.33401/fujma.1107963
Chicago OZTURK MAHPEYKER,Büyükkaya Abdurrahman On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. Fundamental journal of mathematics and applications (Online) 5, no.4 (2022): 210 - 227. 10.33401/fujma.1107963
MLA OZTURK MAHPEYKER,Büyükkaya Abdurrahman On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. Fundamental journal of mathematics and applications (Online), vol.5, no.4, 2022, ss.210 - 227. 10.33401/fujma.1107963
AMA OZTURK M,Büyükkaya A On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. Fundamental journal of mathematics and applications (Online). 2022; 5(4): 210 - 227. 10.33401/fujma.1107963
Vancouver OZTURK M,Büyükkaya A On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces. Fundamental journal of mathematics and applications (Online). 2022; 5(4): 210 - 227. 10.33401/fujma.1107963
IEEE OZTURK M,Büyükkaya A "On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces." Fundamental journal of mathematics and applications (Online), 5, ss.210 - 227, 2022. 10.33401/fujma.1107963
ISNAD OZTURK, MAHPEYKER - Büyükkaya, Abdurrahman. "On Some Fixed Point Theorems for $mathcal{G} (Sigma, vartheta, Xi )-$Contractions in Modular $b-$Metric Spaces". Fundamental journal of mathematics and applications (Online) 5/4 (2022), 210-227. https://doi.org/10.33401/fujma.1107963
Sayfa Oluşturulma Tarihi
24-04-2024 5:15

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