Research Article
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Year 2020, Volume: 69 Issue: 2, 1405 - 1417, 31.12.2020
https://doi.org/10.31801/cfsuasmas.727181

Abstract

References

  • Al-Thagafi, M. A., Shahzad, N., Best proximity pairs and equilibrium pairs for Kakutani multimaps, Nonlinear Anal., 70 (2009), 1209-1216.
  • Altun, I., Aslantas, M., Sahin, H., Best proximity point results for p-proximal contractions, Acta Math. Hungar., (2020), https://doi.org/10.1007/s10474-020-01036-3.
  • Argoubi, H., Samet, B., Vetro, C., Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl., 8 (6) (2015), 1082-1094.
  • Aydi, H., Felhi, A., On best proximity points for various α-proximal contractions on metric-like spaces, J. Nonlinear Sci. Appl., 9 (2016), 5202--5218.
  • Aydi, H., Felhi, A., Best proximity points for cyclic Kannan-Chatterjea-Ćirić type contractions on metric-like spaces, J. Nonlinear Sci. Appl., 9 (2016), 2458--2466.
  • Caballero, J., Harjani, J., Sadarangani, K., A best proximity point theorem for Geraghty-contractions, Fixed Point Theory Appl., 2012:231 (2012).
  • Eldred, A. A., Veeramani, P., Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2) (2006), 1001-1006.
  • Fang, S. C., Petersen, E. L., Generalized variational inequalities, J. Optim. Theory Appl., 38 (1982), 363-383.
  • Hussain, N., Kutbi, M. A., Salimi, P., Best proximity point results for modified α-ψ-proximal rational contractions, Abstr. Appl. Anal., 2013, Article ID 927457 (2013).
  • Işık, H., Aydi, H., Mlaiki, N., Radenović, S., Best proximity point results for Geraghty type Z-proximal contractions with an application, Axioms, 8 (3) (2019), 81.
  • Işık, H., Sezen, M. S., Vetro, C., ϕ-Best proximity point theorems and applications to variational inequality problems, J. Fixed Point Theory Appl., 19 (4) (2017), 3177-3189.
  • Jleli, M., Samet, B.: Best proximity points for α-ψ-proximal contractive type mappings and application, Bull. Sci. Math., 137 (2013), 977-995.
  • Karapınar, E., Khojasteh, F., An approach to best proximity points results via simulation functions, J. Fixed Point Theory Appl., 19 (2017), 1983-1995.
  • Khojasteh, F., Shukla, S., Radenović, S., A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (6) (2015), 1189-1194.
  • Kinderlehrer, D., Stampacchia, G., An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980.
  • Kumam, P., Aydi, H., Karapınar, E., Sintunavarat, W., Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems, Fixed Point Theory Appl., 2013:242 (2013).
  • Roldan-Lopez-de-Hierro, A. F., Karapınar, E., Roldan-Lopez-de-Hierro, C., Martinez-Moreno, J., Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), 345-355.
  • Sadiq Basha, S., Veeramani, P., Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory, 103 (2000), 119-129.
  • Sahin, H., Aslantas, M., Altun, I., Feng-Liu type approach to best proximity point results, for multivalued mappings, J. Fixed Point Theory Appl., 22 (2020), 11.
  • Samet, B., Best proximity point results in partially ordered metric spaces via simulation functions, Fixed Point Theory Appl., 2015:232 (2015).
  • Sankar Raj, V., A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 74 (14) (2011), 4804-4808.
  • Tchier, F., Vetro, C., Vetro, F., Best approximation and variational inequality problems involving a simulation function, Fixed Point Theory Appl., 2016:26 (2016).
  • Todd, M. J., The Computations of Fixed Points and Applications, Springer, Berlin, 1976.

Best proximity problems for new types of $\mathcal{Z}$-proximal contractions with an application

Year 2020, Volume: 69 Issue: 2, 1405 - 1417, 31.12.2020
https://doi.org/10.31801/cfsuasmas.727181

Abstract

In this study, we establish existence and uniqueness theorems of best proximity points for new types of $\mathcal{Z}$-proximal contractions defined on a complete metric space. The presented results improve and generalize some recent results in the literature. Several examples are constructed to demonstrate the generality of our results. As applications of the obtained results, we discuss sufficient conditions to ensure the existence of a unique solution for a variational inequality problem.

References

  • Al-Thagafi, M. A., Shahzad, N., Best proximity pairs and equilibrium pairs for Kakutani multimaps, Nonlinear Anal., 70 (2009), 1209-1216.
  • Altun, I., Aslantas, M., Sahin, H., Best proximity point results for p-proximal contractions, Acta Math. Hungar., (2020), https://doi.org/10.1007/s10474-020-01036-3.
  • Argoubi, H., Samet, B., Vetro, C., Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl., 8 (6) (2015), 1082-1094.
  • Aydi, H., Felhi, A., On best proximity points for various α-proximal contractions on metric-like spaces, J. Nonlinear Sci. Appl., 9 (2016), 5202--5218.
  • Aydi, H., Felhi, A., Best proximity points for cyclic Kannan-Chatterjea-Ćirić type contractions on metric-like spaces, J. Nonlinear Sci. Appl., 9 (2016), 2458--2466.
  • Caballero, J., Harjani, J., Sadarangani, K., A best proximity point theorem for Geraghty-contractions, Fixed Point Theory Appl., 2012:231 (2012).
  • Eldred, A. A., Veeramani, P., Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2) (2006), 1001-1006.
  • Fang, S. C., Petersen, E. L., Generalized variational inequalities, J. Optim. Theory Appl., 38 (1982), 363-383.
  • Hussain, N., Kutbi, M. A., Salimi, P., Best proximity point results for modified α-ψ-proximal rational contractions, Abstr. Appl. Anal., 2013, Article ID 927457 (2013).
  • Işık, H., Aydi, H., Mlaiki, N., Radenović, S., Best proximity point results for Geraghty type Z-proximal contractions with an application, Axioms, 8 (3) (2019), 81.
  • Işık, H., Sezen, M. S., Vetro, C., ϕ-Best proximity point theorems and applications to variational inequality problems, J. Fixed Point Theory Appl., 19 (4) (2017), 3177-3189.
  • Jleli, M., Samet, B.: Best proximity points for α-ψ-proximal contractive type mappings and application, Bull. Sci. Math., 137 (2013), 977-995.
  • Karapınar, E., Khojasteh, F., An approach to best proximity points results via simulation functions, J. Fixed Point Theory Appl., 19 (2017), 1983-1995.
  • Khojasteh, F., Shukla, S., Radenović, S., A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (6) (2015), 1189-1194.
  • Kinderlehrer, D., Stampacchia, G., An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980.
  • Kumam, P., Aydi, H., Karapınar, E., Sintunavarat, W., Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems, Fixed Point Theory Appl., 2013:242 (2013).
  • Roldan-Lopez-de-Hierro, A. F., Karapınar, E., Roldan-Lopez-de-Hierro, C., Martinez-Moreno, J., Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), 345-355.
  • Sadiq Basha, S., Veeramani, P., Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory, 103 (2000), 119-129.
  • Sahin, H., Aslantas, M., Altun, I., Feng-Liu type approach to best proximity point results, for multivalued mappings, J. Fixed Point Theory Appl., 22 (2020), 11.
  • Samet, B., Best proximity point results in partially ordered metric spaces via simulation functions, Fixed Point Theory Appl., 2015:232 (2015).
  • Sankar Raj, V., A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 74 (14) (2011), 4804-4808.
  • Tchier, F., Vetro, C., Vetro, F., Best approximation and variational inequality problems involving a simulation function, Fixed Point Theory Appl., 2016:26 (2016).
  • Todd, M. J., The Computations of Fixed Points and Applications, Springer, Berlin, 1976.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Hüseyin Işık 0000-0001-7558-4088

Hassen Aydi 0000-0003-4606-7211

Publication Date December 31, 2020
Submission Date April 26, 2020
Acceptance Date August 23, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Işık, H., & Aydi, H. (2020). Best proximity problems for new types of $\mathcal{Z}$-proximal contractions with an application. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1405-1417. https://doi.org/10.31801/cfsuasmas.727181
AMA Işık H, Aydi H. Best proximity problems for new types of $\mathcal{Z}$-proximal contractions with an application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1405-1417. doi:10.31801/cfsuasmas.727181
Chicago Işık, Hüseyin, and Hassen Aydi. “Best Proximity Problems for New Types of $\mathcal{Z}$-Proximal Contractions With an Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1405-17. https://doi.org/10.31801/cfsuasmas.727181.
EndNote Işık H, Aydi H (December 1, 2020) Best proximity problems for new types of $\mathcal{Z}$-proximal contractions with an application. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1405–1417.
IEEE H. Işık and H. Aydi, “Best proximity problems for new types of $\mathcal{Z}$-proximal contractions with an application”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1405–1417, 2020, doi: 10.31801/cfsuasmas.727181.
ISNAD Işık, Hüseyin - Aydi, Hassen. “Best Proximity Problems for New Types of $\mathcal{Z}$-Proximal Contractions With an Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1405-1417. https://doi.org/10.31801/cfsuasmas.727181.
JAMA Işık H, Aydi H. Best proximity problems for new types of $\mathcal{Z}$-proximal contractions with an application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1405–1417.
MLA Işık, Hüseyin and Hassen Aydi. “Best Proximity Problems for New Types of $\mathcal{Z}$-Proximal Contractions With an Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1405-17, doi:10.31801/cfsuasmas.727181.
Vancouver Işık H, Aydi H. Best proximity problems for new types of $\mathcal{Z}$-proximal contractions with an application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1405-17.

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

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