Research Article
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Year 2022, Volume: 5 Issue: 4, 487 - 498, 30.12.2022

Leta Bekere Kumssa

Abstract

References

  • A. Abkar, M. Gabeleh, Global optimal solutions of non-cyclic mappings in metric spaces, J. Optim. Theory Appl. 153 (2012) 298-305.
  • A. Abkar, M. Gabeleh, Best proximity points of non-self mappings. Top 21 (2013) 287-295.
  • M.A. Al-Thaga, N. Shahzad, Convergence and existence results for best proximity points. Nonlinear Anal. 70(2009) 3665-3671.
  • S. Aleksic, Z. D. Mitrovic, and S. Radenovic, A fixed point theorem of Jungck in bv(s)-metric spaces. Period. Math. Hung. 77(2) (2018) 224-231.
  • E. Altiparmak and I. Karahan, Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial bv(s)-Metric Spaces. Sahand Communications in Mathematical Analysis. 18(2) (2021) 45-62.
  • E. Altiparmak and I. Karahan, Fixed point results in partially ordered partial bv(s)-metric spaces. International Journal of Nonlinear Analysis and Applications. 12(2) (2021) 35-52.
  • S. Banach, Sur les operations dans les ensembles abstraits et leur application auxequations integrales. Fundam. Math. 3(1922) 133-181.
  • S.S. Basha, Best proximity points optimal solutions. J. Optim. Theory Appl. 151(2011) 210-216.
  • S. S. Basha, Discrete optimization in partially ordered sets. J. Glob. Optim. 54(2012) 511-517.
  • P. Charoensawan, Common fixed point theorems for Geraghty's type contraction mapping with two generalized metrics endowed with a directed graph in JS-metric spaces. Carpathian Journal of Mathematics. 34(2018) 305-312.
  • S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis. 1(1) (1993) 5-11.
  • F. Dong, P. Ji, Sheng, and X. Wang, Pata-Type Fixed Point Results in bv(s)-Metric Spaces. International Journal of Analysis and Applications. 17(3) (2019) 342-360.
  • T. Doˇsenovi´c, Z. Kadelburg, D. Mitrovi´c, and S. Radenovi´c, New xed point results in bv(s)-metric spaces. Mathematica Slovaca. 70(2) (2020) 441-452.
  • D. Dukic, Z. Kadelburg, and S. Radenovic, Fixed point of Geraghty-type mappings in various generalized metric spaces. Abstr Appl Anal. in (2011).
  • R. George, S. Radenovi´c, K. P. Reshma, and S. Shukla, Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 8(6) (2015) 1005-1013. [ M. Geraghty, On contractive mappings, Proc. Am. Math. Soc. 40(1973) 604-608.
  • M. Gordji, M. Ramezani, Y. Cho, and S. Pirbavafa, A generalization of Geraghty's theorem in partially ordered metric spaces and applications to ordinary differential equations. Fixed Point Theory and Applications. 74(1) 2012.
  • J. Hamzehnejadi, and R. Lashkaripour, Best proximity points for generalized α − ϕ−Geraghty proximal contraction mappings and its application. Fixed point theory and applications. (2016) 2016:72 1-13.
  • M. Jleli, and B. Samet, Best proximity points for α − ψ-proximal contractive type mappings and applications. Bull.Sci.Math. 137(8) (2013) 977-995.
  • Z. Kadelburg, P. Kumam, S. Radenovi¢, and W. Sintunavarat, Common coupled fixed point theorems for Geraghty-type contraction mappings using monotone property. Fixed Point Theory and Applications. 27(2015).
  • E. Karapinar, P. Kumam, and P. Salimi, On α-ψ-Meir-Keeler contractive mappings. Fixed Point Theory and Applications. 94(1) (2013) 1-12.
  • P. Kumam, P. Salimi, and C. Vetro, Best proximity point results for modified α-proximal C-contraction mappings. Fixed Point Theory and Applications. (2014) 2014:99.
  • Z. D. Mitrovi´c, and S. Radenovi´c, The Banach and Reich contractions in bv(s)-metric spaces. J. Fixed Point Theory Appl. 19(2017) 3087-3095.
  • B. Samet C. Vetro, and P. Vetro, Fixed point theorems for α − ψ-contractive type mappings. Nonlinear Anal. 75(4) (2012) 2154-2165.
  • J. Zhang, Y. Su, and Q. Cheng, A note on A best proximity point theorem for Geraghty-contractions. Fixed Point Theory Appl. (2013) 2013:99.

GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN bv(s) -METRIC SPACES

Year 2022, Volume: 5 Issue: 4, 487 - 498, 30.12.2022

Leta Bekere Kumssa

Abstract

In this article, we will determine the best proximity point results for the Geraghty proximal contraction type mappings in a more general space called the bv(s)-metric space, and prove the existence of the best proximity point for such mappings which satisfy the RJ-Property. We also derive some consequences as a justification for the validity of the main result. The results presented here extend, generalize, and integrate many previous results in the literature.

Keywords

best proximity point Geraghty proximal contraction RJ-Property bv(s) metric space

References

  • A. Abkar, M. Gabeleh, Global optimal solutions of non-cyclic mappings in metric spaces, J. Optim. Theory Appl. 153 (2012) 298-305.
  • A. Abkar, M. Gabeleh, Best proximity points of non-self mappings. Top 21 (2013) 287-295.
  • M.A. Al-Thaga, N. Shahzad, Convergence and existence results for best proximity points. Nonlinear Anal. 70(2009) 3665-3671.
  • S. Aleksic, Z. D. Mitrovic, and S. Radenovic, A fixed point theorem of Jungck in bv(s)-metric spaces. Period. Math. Hung. 77(2) (2018) 224-231.
  • E. Altiparmak and I. Karahan, Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial bv(s)-Metric Spaces. Sahand Communications in Mathematical Analysis. 18(2) (2021) 45-62.
  • E. Altiparmak and I. Karahan, Fixed point results in partially ordered partial bv(s)-metric spaces. International Journal of Nonlinear Analysis and Applications. 12(2) (2021) 35-52.
  • S. Banach, Sur les operations dans les ensembles abstraits et leur application auxequations integrales. Fundam. Math. 3(1922) 133-181.
  • S.S. Basha, Best proximity points optimal solutions. J. Optim. Theory Appl. 151(2011) 210-216.
  • S. S. Basha, Discrete optimization in partially ordered sets. J. Glob. Optim. 54(2012) 511-517.
  • P. Charoensawan, Common fixed point theorems for Geraghty's type contraction mapping with two generalized metrics endowed with a directed graph in JS-metric spaces. Carpathian Journal of Mathematics. 34(2018) 305-312.
  • S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis. 1(1) (1993) 5-11.
  • F. Dong, P. Ji, Sheng, and X. Wang, Pata-Type Fixed Point Results in bv(s)-Metric Spaces. International Journal of Analysis and Applications. 17(3) (2019) 342-360.
  • T. Doˇsenovi´c, Z. Kadelburg, D. Mitrovi´c, and S. Radenovi´c, New xed point results in bv(s)-metric spaces. Mathematica Slovaca. 70(2) (2020) 441-452.
  • D. Dukic, Z. Kadelburg, and S. Radenovic, Fixed point of Geraghty-type mappings in various generalized metric spaces. Abstr Appl Anal. in (2011).
  • R. George, S. Radenovi´c, K. P. Reshma, and S. Shukla, Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 8(6) (2015) 1005-1013. [ M. Geraghty, On contractive mappings, Proc. Am. Math. Soc. 40(1973) 604-608.
  • M. Gordji, M. Ramezani, Y. Cho, and S. Pirbavafa, A generalization of Geraghty's theorem in partially ordered metric spaces and applications to ordinary differential equations. Fixed Point Theory and Applications. 74(1) 2012.
  • J. Hamzehnejadi, and R. Lashkaripour, Best proximity points for generalized α − ϕ−Geraghty proximal contraction mappings and its application. Fixed point theory and applications. (2016) 2016:72 1-13.
  • M. Jleli, and B. Samet, Best proximity points for α − ψ-proximal contractive type mappings and applications. Bull.Sci.Math. 137(8) (2013) 977-995.
  • Z. Kadelburg, P. Kumam, S. Radenovi¢, and W. Sintunavarat, Common coupled fixed point theorems for Geraghty-type contraction mappings using monotone property. Fixed Point Theory and Applications. 27(2015).
  • E. Karapinar, P. Kumam, and P. Salimi, On α-ψ-Meir-Keeler contractive mappings. Fixed Point Theory and Applications. 94(1) (2013) 1-12.
  • P. Kumam, P. Salimi, and C. Vetro, Best proximity point results for modified α-proximal C-contraction mappings. Fixed Point Theory and Applications. (2014) 2014:99.
  • Z. D. Mitrovi´c, and S. Radenovi´c, The Banach and Reich contractions in bv(s)-metric spaces. J. Fixed Point Theory Appl. 19(2017) 3087-3095.
  • B. Samet C. Vetro, and P. Vetro, Fixed point theorems for α − ψ-contractive type mappings. Nonlinear Anal. 75(4) (2012) 2154-2165.
  • J. Zhang, Y. Su, and Q. Cheng, A note on A best proximity point theorem for Geraghty-contractions. Fixed Point Theory Appl. (2013) 2013:99.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Leta Bekere Kumssa 0000-0001-6908-0203

Publication Date December 30, 2022
Published in Issue Year 2022 Volume: 5 Issue: 4

Cite

APA Bekere Kumssa, L. (2022). GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN bv(s) -METRIC SPACES. Results in Nonlinear Analysis, 5(4), 487-498. https://doi.org/10.53006/rna.1065458
AMA Bekere Kumssa L. GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN bv(s) -METRIC SPACES. RNA. December 2022;5(4):487-498. doi:10.53006/rna.1065458
Chicago Bekere Kumssa, Leta. “GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN Bv(s) -METRIC SPACES”. Results in Nonlinear Analysis 5, no. 4 (December 2022): 487-98. https://doi.org/10.53006/rna.1065458.
EndNote Bekere Kumssa L (December 1, 2022) GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN bv(s) -METRIC SPACES. Results in Nonlinear Analysis 5 4 487–498.
IEEE L. Bekere Kumssa, “GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN bv(s) -METRIC SPACES”, RNA, vol. 5, no. 4, pp. 487–498, 2022, doi: 10.53006/rna.1065458.
ISNAD Bekere Kumssa, Leta. “GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN Bv(s) -METRIC SPACES”. Results in Nonlinear Analysis 5/4 (December2022), 487-498. https://doi.org/10.53006/rna.1065458.
JAMA Bekere Kumssa L. GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN bv(s) -METRIC SPACES. RNA. 2022;5:487–498.
MLA Bekere Kumssa, Leta. “GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN Bv(s) -METRIC SPACES”. Results in Nonlinear Analysis, vol. 5, no. 4, 2022, pp. 487-98, doi:10.53006/rna.1065458.
Vancouver Bekere Kumssa L. GERAGHTY PROXIMAL CONTRACTION TYPE MAPPINGS AND RJ-PROPERTY IN bv(s) -METRIC SPACES. RNA. 2022;5(4):487-98.