Research Article
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Best Proximity Point Results on Strong b-Metric Spaces

Year 2021, Issue: 34, 28 - 36, 30.03.2021

Abstract

In the present paper, we prove the two best proximity point results on strong b-metric spaces with coefficient λ by introducing two new concepts which are named as BW b-contraction and proximal BW b-contraction. Thus, we generalise and improve many results available in the literature. To support our main results, some nontrivial and illustrative examples are given.

References

  • S. Banach, Sur Les Operations Dans Les Ensembles Abstraits et Leur Applications Aux equations Integrales, Fundamenta Mathematicae 3(1) (1922) 133-181.
  • M. Abbas, T. Nazir, Fixed Point of Generalized Weakly Contractive Mappings in Ordered Partial Metric Spaces, Fixed Point Theory and Application 2012(1) (2012) 1-19.
  • M. Aslantaş, H. Şahin, D. Türkoğlu, Some Caristi Type Fixed Point Theorems, The Journal of Analysis (2020) 1-15. https://doi.org/10.1007/s41478-020-00248-8
  • L. Ciric, B. Samet, H. Aydi, C. Vetro, Common Fixed Points of Generalized Contractions on Partial Metric Spaces and An Application, Applied Mathematics and Computation 218(6) (2011) 2398-2406.
  • M. Riaz, S. T. Tehrim, A Robust Extension of VIKOR Method for Bipolar Fuzzy Sets Using Connection Numbers of SPA Theory Based Metric Spaces, Artificial Intelligence Review 54 (2020) 561-591.
  • M. Riaz, S. T. Tehrim, Bipolar Fuzzy Soft Mappings with Application to Bipolar Disorders, International Journal of Biomathematics 12(07) (2019) 1-31.
  • M. Riaz, F. Smarandache, A. Firdous, A. Fakhar, On Soft Rough Topology with Multi-attribute Group Decision Making, Mathematics 7(1) (2019) 1-18.
  • S. T. Tehrim, M. Riaz, A Novel Extension of TOPSIS to MCGDM with Bipolar Neutrosophic Soft Topology, Journal of Intelligent and Fuzzy Systems 37(4) (2019) 5531-5549.
  • M. Riaz, M. R. Hashmi, Fixed Points of Fuzzy Neutrosophic Soft Mapping with Decision-making, Fixed Point Theory and Applications 2018(7) (2018) 1-10.
  • S. Romaguera, Fixed Point Theorems for Generalized Contractions on Partial Metric Spaces, Topology and Its Applications 159(1) (2012) 194-199.
  • S. Romaguera, A Kirk Type Characterization of Completeness for Partial Metric Spaces, Fixed Point Theory and Applications (2010) Article ID 493298, 6 pages.
  • D. W. Boyd, J. S. Wong, On Nonlinear Contraction, Proceedings of the American Mathematical Society 20(2) (1969) 458-464.
  • S. Czerwik, Contraction Mappings in b-metric Spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1(1) (1993) 5-11.
  • S. Czerwik, Nonlinear Set-valued Contraction Mappings in b-metric Spaces, Atti del Seminario Matematico e Fisico dell'Universita di Modena 46 (1998) 263-276.
  • W. Kirk, N. Shahzad, Fixed Point Theory in Distance Spaces, Springer, Cham, 2014.
  • İ. Altun, M. Aslantaş, H. Sahin, Best Proximity Point Results for p-proximal Contractions, Acta Mathematica Hungarica 162 (2020) 393-402.
  • M. Aslantaş, H. Şahin, İ. Altun, Best Proximity Point Theorems for Cyclic p-contractions with Some Consequences and Applications, Nonlinear Analysis: Modelling and Control 26(1) (2021) 113-129.
  • H. Şahin, Best Proximity Point Theory on Vector Metric Spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70(1) 2021 130-142.
  • H. Şahin, M. Aslantaş, İ. Altun, Feng-Liu Type Approach to Best Proximity Point Results for Multivalued Mappings, Journal of Fixed Point Theory and Applications 22(11) (2020) 1-13.
  • M. Gabeleh, Global Optimal Solutions of Non-self Mappings, Scientific Bulletin, Series A: Applied Mathematics and Physics 75(3) (2013) 67-74.
  • S. S. Basha, Best Proximity Points: Optimal Solutions, Journal of Optimization Theory and Applications 151 (2011) 210-216.
Year 2021, Issue: 34, 28 - 36, 30.03.2021

Abstract

References

  • S. Banach, Sur Les Operations Dans Les Ensembles Abstraits et Leur Applications Aux equations Integrales, Fundamenta Mathematicae 3(1) (1922) 133-181.
  • M. Abbas, T. Nazir, Fixed Point of Generalized Weakly Contractive Mappings in Ordered Partial Metric Spaces, Fixed Point Theory and Application 2012(1) (2012) 1-19.
  • M. Aslantaş, H. Şahin, D. Türkoğlu, Some Caristi Type Fixed Point Theorems, The Journal of Analysis (2020) 1-15. https://doi.org/10.1007/s41478-020-00248-8
  • L. Ciric, B. Samet, H. Aydi, C. Vetro, Common Fixed Points of Generalized Contractions on Partial Metric Spaces and An Application, Applied Mathematics and Computation 218(6) (2011) 2398-2406.
  • M. Riaz, S. T. Tehrim, A Robust Extension of VIKOR Method for Bipolar Fuzzy Sets Using Connection Numbers of SPA Theory Based Metric Spaces, Artificial Intelligence Review 54 (2020) 561-591.
  • M. Riaz, S. T. Tehrim, Bipolar Fuzzy Soft Mappings with Application to Bipolar Disorders, International Journal of Biomathematics 12(07) (2019) 1-31.
  • M. Riaz, F. Smarandache, A. Firdous, A. Fakhar, On Soft Rough Topology with Multi-attribute Group Decision Making, Mathematics 7(1) (2019) 1-18.
  • S. T. Tehrim, M. Riaz, A Novel Extension of TOPSIS to MCGDM with Bipolar Neutrosophic Soft Topology, Journal of Intelligent and Fuzzy Systems 37(4) (2019) 5531-5549.
  • M. Riaz, M. R. Hashmi, Fixed Points of Fuzzy Neutrosophic Soft Mapping with Decision-making, Fixed Point Theory and Applications 2018(7) (2018) 1-10.
  • S. Romaguera, Fixed Point Theorems for Generalized Contractions on Partial Metric Spaces, Topology and Its Applications 159(1) (2012) 194-199.
  • S. Romaguera, A Kirk Type Characterization of Completeness for Partial Metric Spaces, Fixed Point Theory and Applications (2010) Article ID 493298, 6 pages.
  • D. W. Boyd, J. S. Wong, On Nonlinear Contraction, Proceedings of the American Mathematical Society 20(2) (1969) 458-464.
  • S. Czerwik, Contraction Mappings in b-metric Spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1(1) (1993) 5-11.
  • S. Czerwik, Nonlinear Set-valued Contraction Mappings in b-metric Spaces, Atti del Seminario Matematico e Fisico dell'Universita di Modena 46 (1998) 263-276.
  • W. Kirk, N. Shahzad, Fixed Point Theory in Distance Spaces, Springer, Cham, 2014.
  • İ. Altun, M. Aslantaş, H. Sahin, Best Proximity Point Results for p-proximal Contractions, Acta Mathematica Hungarica 162 (2020) 393-402.
  • M. Aslantaş, H. Şahin, İ. Altun, Best Proximity Point Theorems for Cyclic p-contractions with Some Consequences and Applications, Nonlinear Analysis: Modelling and Control 26(1) (2021) 113-129.
  • H. Şahin, Best Proximity Point Theory on Vector Metric Spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70(1) 2021 130-142.
  • H. Şahin, M. Aslantaş, İ. Altun, Feng-Liu Type Approach to Best Proximity Point Results for Multivalued Mappings, Journal of Fixed Point Theory and Applications 22(11) (2020) 1-13.
  • M. Gabeleh, Global Optimal Solutions of Non-self Mappings, Scientific Bulletin, Series A: Applied Mathematics and Physics 75(3) (2013) 67-74.
  • S. S. Basha, Best Proximity Points: Optimal Solutions, Journal of Optimization Theory and Applications 151 (2011) 210-216.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Mustafa Aslantaş 0000-0003-4338-3518

Publication Date March 30, 2021
Submission Date August 20, 2020
Published in Issue Year 2021 Issue: 34

Cite

APA Aslantaş, M. (2021). Best Proximity Point Results on Strong b-Metric Spaces. Journal of New Theory(34), 28-36.
AMA Aslantaş M. Best Proximity Point Results on Strong b-Metric Spaces. JNT. March 2021;(34):28-36.
Chicago Aslantaş, Mustafa. “Best Proximity Point Results on Strong B-Metric Spaces”. Journal of New Theory, no. 34 (March 2021): 28-36.
EndNote Aslantaş M (March 1, 2021) Best Proximity Point Results on Strong b-Metric Spaces. Journal of New Theory 34 28–36.
IEEE M. Aslantaş, “Best Proximity Point Results on Strong b-Metric Spaces”, JNT, no. 34, pp. 28–36, March 2021.
ISNAD Aslantaş, Mustafa. “Best Proximity Point Results on Strong B-Metric Spaces”. Journal of New Theory 34 (March 2021), 28-36.
JAMA Aslantaş M. Best Proximity Point Results on Strong b-Metric Spaces. JNT. 2021;:28–36.
MLA Aslantaş, Mustafa. “Best Proximity Point Results on Strong B-Metric Spaces”. Journal of New Theory, no. 34, 2021, pp. 28-36.
Vancouver Aslantaş M. Best Proximity Point Results on Strong b-Metric Spaces. JNT. 2021(34):28-36.


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