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On $\theta$-convex contractive mappings with application to integral equations

Yıl 2024, Cilt: 73 Sayı: 1, 13 - 24, 16.03.2024

Merve Özkan Murat Özdemir İsa Yildirim

https://doi.org/10.31801/cfsuasmas.1302945

Öz

The fundamental goal of our paper is to study $\theta$-convex contractive mappings in metric spaces. We demonstrate some fixed point results for such mappings. Also, we give an application to integral equations of our results. Consequently, our results encompass numerous generalizations of the Banach contraction principle on metric space.

Anahtar Kelimeler

Integral equation fixed point convex contraction θ-contraction

Kaynakça

  • Banach, S., Sur les operationes dans les ensembles abstraits et leur application aux equation integrale, Fundam. Math., 3(1) (1922), 133-181.
  • Berinde, V., Pacurar, M., Fixed points and continuity of almost contractions, Fixed Point Theory, 9(1) (2008), 23–34.
  • Berinde, V., Approximating fixed points of weak contraction using the Picard iteration, Nonlinear Anal. Forum, 9 (2004), 43–53.
  • Berinde, M., Berinde, V., On general class of multivalued weakly Picard mappings, J. Nonlinear Sci. Appl., 326(2) (2007), 772–782. https://doi.org/10.1016/j.jmaa.2006.03.016
  • Jleli, M., Samet, B., A new generalization of the Banach contractive principle, J. Inequal. Appl., 38 (2014). https://doi.org/10.1186/1029-242X-2014-38
  • Jleli, M., Karapınar, E., Samet, B., Further generalizations of the Banach contraction principle, J. Inequal. Appl., 439 (2014). https://doi.org/10.1186/1029-242X-2014-439
  • Hussain, N., Parvaneh, V., Samet, B., Vetro, C., Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory Appl., 17 (2015). https://doi.org/10.1186/s13663-015-0433-z
  • Imdad, M., Alfaqih, W. M., Khan, I. A., Weak $\theta$−contractions and some fixed point results with applications to fractal theory, Adv. Differ. Equ., 439 (2018). https://doi.org/10.1186/s13662-018-1900-8
  • Istratescu, V. I., Some fixed point theorems for convex contraction mappings and convex non-expansive mapping, Libertas Mathematica, 1 (1981), 151–163.
  • Istratescu, V. I., Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters-I, Ann. Mat. Pura Appl., 130 (1982), 89–104. https://doi.org/10.1007/BF01761490
  • Istratescu, V. I., Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters-II, Ann. Mat. Pura Appl., 134 (1983), 327–362. https://doi.org/10.1007/BF01773511
  • Alghamdi, M. A., Alnafei, S. H., Radenovic, S., Shahzad, N., Fixed point theorems for convex contraction mappings on cone metric spaces, Math. Comput. Model., 54 (2011), no. 9-10, 2020–2026. https://doi.org/10.1016/j.mcm.2011.05.010
  • Ampadu, C. K. B., On the analogue of the convex contraction mapping theorem for tricyclic convex contraction mapping of order 2 in b-metric space, J. Global Research in Math. Archives, 4(6) (2017), 1–5.
  • Ampadu, C. K. B., Some fixed point theory results for convex contraction mapping of order 2, JP J. Fixed Point Theory Appl., 12(2-3) (2017), 81–130.
  • Bisht, R. K., Hussain, N., A note on convex contraction mappings and discontinuity at fixed point, J. Math. Anal., 8(4) (2017), 90-96.
  • Bisht, R. K., Rakocevic, V., Fixed points of convex and generalized convex contractions, Rendiconti Del Circolo Matematico Di Palermo Series 2, 69 (2020), 21-28. https://doi.org/10.1007/s12215-018-0386-2
  • Georgescu, F., IFS consisting of generalized convex contractions, An. Stiint. Univ. Ovidius Constant., 25(1) (2017), 77–86, https://doi.org/10.1515/auom-2017-0007
  • Khan, M. S., Singh, Y. M., Maniu, G., Postolache, M., On generalized convex contractions of type−2 in b-metric and 2−metric spaces, J. Nonlinear Sci. Appl., 10 (2017), 2902–2913. https://doi.org/10.22436/jnsa.010.06.05
  • Khan, M. S., Singh, Y. M., Maniu, G., Postolache, M., On $(\alpha, p)$−convex contraction and asymptotic regularity, J. Math. Comput. Sci., 18 (2018), 132–145. https://doi.org/10.22436/jmcs.018.02.01
  • Karapınar, E., Fulga, A., Petrusel, A., On Istratescu type contractions in b−metric spaces, Mathematics, 8(3) (2020), 388. https://doi.org/10.3390/math8030388
  • Latif, A., Sintunavarat, W., Ninsri, A., Approximate fixed point theorems for partial generalized convex contraction mappings in a−complete metric spaces, Taiwanese J. Math., 19(1) (2015), 315–333. https://doi.org/10.11650/tjm.19.2015.4746
  • Miandarag, M. A., Postolache, M., Rezapour, S., Approximate fixed points of generalizes convex contractions, Fixed Point Theory Appl., 255 (2013), 1–8. https://doi.org/ 10.1186/1687-1812-2013-255
  • Miculescu, R., Mihail, A., A generalization of Istratescu’s fixed piont theorem for convex contractions, Fixed Point Theory, 18(2) (2017), 689-702. https://doi.org/10.24193/fptro.2017.2.55
  • Singh, Y. M., Khan, M. S., Kang, S. M., F-Convex contraction via admissible mapping and related fixed point theorems with an application, Mathematics, 6(6) (2018), 105. https://doi.org/10.3390/math6060105
  • Ciric, L. B., Generalized contractions and fixed point theorems, Publ. Inst. Math., 12(26) (1971), 19–26, https://doi.org/10.2307/2039517
  • Gabeleh, M.,Vetro, C., A best proximity point approach to existence of solutions for a system of ordinary differential equations, Bull. Belg. Math. Soc., 26(4) (2019), 493-503. https://doi.org/10.36045/bbms/1576206350
  • Asadi, M., Gabeleh M., Vetro, C., A new approach to the generalization of Darbo’s fixed point problem by using simulation functions with application to integral equations, Results Math., 74(86) (2019), 1-15. https://doi.org/10.1007/s00025-019-1010-2

Yıl 2024, Cilt: 73 Sayı: 1, 13 - 24, 16.03.2024

Merve Özkan Murat Özdemir İsa Yildirim

https://doi.org/10.31801/cfsuasmas.1302945

Öz

Kaynakça

  • Banach, S., Sur les operationes dans les ensembles abstraits et leur application aux equation integrale, Fundam. Math., 3(1) (1922), 133-181.
  • Berinde, V., Pacurar, M., Fixed points and continuity of almost contractions, Fixed Point Theory, 9(1) (2008), 23–34.
  • Berinde, V., Approximating fixed points of weak contraction using the Picard iteration, Nonlinear Anal. Forum, 9 (2004), 43–53.
  • Berinde, M., Berinde, V., On general class of multivalued weakly Picard mappings, J. Nonlinear Sci. Appl., 326(2) (2007), 772–782. https://doi.org/10.1016/j.jmaa.2006.03.016
  • Jleli, M., Samet, B., A new generalization of the Banach contractive principle, J. Inequal. Appl., 38 (2014). https://doi.org/10.1186/1029-242X-2014-38
  • Jleli, M., Karapınar, E., Samet, B., Further generalizations of the Banach contraction principle, J. Inequal. Appl., 439 (2014). https://doi.org/10.1186/1029-242X-2014-439
  • Hussain, N., Parvaneh, V., Samet, B., Vetro, C., Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory Appl., 17 (2015). https://doi.org/10.1186/s13663-015-0433-z
  • Imdad, M., Alfaqih, W. M., Khan, I. A., Weak $\theta$−contractions and some fixed point results with applications to fractal theory, Adv. Differ. Equ., 439 (2018). https://doi.org/10.1186/s13662-018-1900-8
  • Istratescu, V. I., Some fixed point theorems for convex contraction mappings and convex non-expansive mapping, Libertas Mathematica, 1 (1981), 151–163.
  • Istratescu, V. I., Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters-I, Ann. Mat. Pura Appl., 130 (1982), 89–104. https://doi.org/10.1007/BF01761490
  • Istratescu, V. I., Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters-II, Ann. Mat. Pura Appl., 134 (1983), 327–362. https://doi.org/10.1007/BF01773511
  • Alghamdi, M. A., Alnafei, S. H., Radenovic, S., Shahzad, N., Fixed point theorems for convex contraction mappings on cone metric spaces, Math. Comput. Model., 54 (2011), no. 9-10, 2020–2026. https://doi.org/10.1016/j.mcm.2011.05.010
  • Ampadu, C. K. B., On the analogue of the convex contraction mapping theorem for tricyclic convex contraction mapping of order 2 in b-metric space, J. Global Research in Math. Archives, 4(6) (2017), 1–5.
  • Ampadu, C. K. B., Some fixed point theory results for convex contraction mapping of order 2, JP J. Fixed Point Theory Appl., 12(2-3) (2017), 81–130.
  • Bisht, R. K., Hussain, N., A note on convex contraction mappings and discontinuity at fixed point, J. Math. Anal., 8(4) (2017), 90-96.
  • Bisht, R. K., Rakocevic, V., Fixed points of convex and generalized convex contractions, Rendiconti Del Circolo Matematico Di Palermo Series 2, 69 (2020), 21-28. https://doi.org/10.1007/s12215-018-0386-2
  • Georgescu, F., IFS consisting of generalized convex contractions, An. Stiint. Univ. Ovidius Constant., 25(1) (2017), 77–86, https://doi.org/10.1515/auom-2017-0007
  • Khan, M. S., Singh, Y. M., Maniu, G., Postolache, M., On generalized convex contractions of type−2 in b-metric and 2−metric spaces, J. Nonlinear Sci. Appl., 10 (2017), 2902–2913. https://doi.org/10.22436/jnsa.010.06.05
  • Khan, M. S., Singh, Y. M., Maniu, G., Postolache, M., On $(\alpha, p)$−convex contraction and asymptotic regularity, J. Math. Comput. Sci., 18 (2018), 132–145. https://doi.org/10.22436/jmcs.018.02.01
  • Karapınar, E., Fulga, A., Petrusel, A., On Istratescu type contractions in b−metric spaces, Mathematics, 8(3) (2020), 388. https://doi.org/10.3390/math8030388
  • Latif, A., Sintunavarat, W., Ninsri, A., Approximate fixed point theorems for partial generalized convex contraction mappings in a−complete metric spaces, Taiwanese J. Math., 19(1) (2015), 315–333. https://doi.org/10.11650/tjm.19.2015.4746
  • Miandarag, M. A., Postolache, M., Rezapour, S., Approximate fixed points of generalizes convex contractions, Fixed Point Theory Appl., 255 (2013), 1–8. https://doi.org/ 10.1186/1687-1812-2013-255
  • Miculescu, R., Mihail, A., A generalization of Istratescu’s fixed piont theorem for convex contractions, Fixed Point Theory, 18(2) (2017), 689-702. https://doi.org/10.24193/fptro.2017.2.55
  • Singh, Y. M., Khan, M. S., Kang, S. M., F-Convex contraction via admissible mapping and related fixed point theorems with an application, Mathematics, 6(6) (2018), 105. https://doi.org/10.3390/math6060105
  • Ciric, L. B., Generalized contractions and fixed point theorems, Publ. Inst. Math., 12(26) (1971), 19–26, https://doi.org/10.2307/2039517
  • Gabeleh, M.,Vetro, C., A best proximity point approach to existence of solutions for a system of ordinary differential equations, Bull. Belg. Math. Soc., 26(4) (2019), 493-503. https://doi.org/10.36045/bbms/1576206350
  • Asadi, M., Gabeleh M., Vetro, C., A new approach to the generalization of Darbo’s fixed point problem by using simulation functions with application to integral equations, Results Math., 74(86) (2019), 1-15. https://doi.org/10.1007/s00025-019-1010-2
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Merve Özkan 0000-0002-7213-4070

Murat Özdemir 0000-0002-4928-3115

İsa Yildirim 0000-0001-6165-716X

Yayımlanma Tarihi 16 Mart 2024
Gönderilme Tarihi 26 Mayıs 2023
Kabul Tarihi 17 Eylül 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 73 Sayı: 1

Kaynak Göster

APA Özkan, M., Özdemir, M., & Yildirim, İ. (2024). On $\theta$-convex contractive mappings with application to integral equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(1), 13-24. https://doi.org/10.31801/cfsuasmas.1302945
AMA Özkan M, Özdemir M, Yildirim İ. On $\theta$-convex contractive mappings with application to integral equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2024;73(1):13-24. doi:10.31801/cfsuasmas.1302945
Chicago Özkan, Merve, Murat Özdemir, ve İsa Yildirim. “On $\theta$-Convex Contractive Mappings With Application to Integral Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, sy. 1 (Mart 2024): 13-24. https://doi.org/10.31801/cfsuasmas.1302945.
EndNote Özkan M, Özdemir M, Yildirim İ (01 Mart 2024) On $\theta$-convex contractive mappings with application to integral equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 1 13–24.
IEEE M. Özkan, M. Özdemir, ve İ. Yildirim, “On $\theta$-convex contractive mappings with application to integral equations”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 73, sy. 1, ss. 13–24, 2024, doi: 10.31801/cfsuasmas.1302945.
ISNAD Özkan, Merve vd. “On $\theta$-Convex Contractive Mappings With Application to Integral Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/1 (Mart 2024), 13-24. https://doi.org/10.31801/cfsuasmas.1302945.
JAMA Özkan M, Özdemir M, Yildirim İ. On $\theta$-convex contractive mappings with application to integral equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:13–24.
MLA Özkan, Merve vd. “On $\theta$-Convex Contractive Mappings With Application to Integral Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 73, sy. 1, 2024, ss. 13-24, doi:10.31801/cfsuasmas.1302945.
Vancouver Özkan M, Özdemir M, Yildirim İ. On $\theta$-convex contractive mappings with application to integral equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(1):13-24.

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

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