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On two types almost (α,F_{d})-contractions on quasi metric space

Year 2019, Volume: 68 Issue: 2, 1819 - 1830, 01.08.2019
https://doi.org/10.31801/cfsuasmas.419821

Abstract

In this paper, first we introduce two new types almost contractions on quasi metric space named as almost (α,F_{d})-contraction of type (x) and of type (y). Then, taking into account both left and right completeness of quasi metric space, we present some fixed point results for these contractions. We also provide some illustrative and comperative examples.

References

  • Alemany E. and Romaguera, S., On half-completion and bicompletion of quasi-metric spaces, Comment. Math. Univ. Carolin. 37(4), (1996), 749--756.
  • Al-Homidan, S., Ansari, Q. H.and Yao, J. C., Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory, Nonlinear Anal. 69(1), (2008), 126--139.
  • Altun, I., Olgun M. and Mınak G., Classification of completeness of quasi metric space and some new fixed point results, Nonlinear Functional Analysis and Applications 22(2), (2017), 371--384.
  • Altun, I., Mınak G. and Dağ H., Multivalued F-contractions on complete metric space, J. Nonlinear Convex Anal. 16(4), (2015), 659--666.
  • Altun, I., Olgun M. and Mınak, G., A new approach to the Assad-Kirk fixed point theorem, J. Fixed Point Theory Appl. 18(1), (2016), 201--212.
  • Altun, I., Olgun M. and Mınak G., On a new class of multivalued weakly Picard operators on complete metric spaces, Taiwanese J. Math. 19(3), (2015), 659--672.
  • Ali M. U., Kamran T. and Shahzad N., Best proximity point for α-ψ-proximal contractive multimaps, Abstr. Appl. Anal. 2014 (2014), 6 pages.
  • Alegre C., Marin J. and Romeguera S., A fixed point theorem for generalized contractions involving ω-distances on complete quasi-metric spaces, Fixed Point Theory Appl. 2014 (2014), 8 pages.
  • Cobzaş, S., Completeness in quasi-metric spaces and Ekeland variational principle, Topology Appl. 158(2011), 1073--1084.
  • Cobzaş, S., Functional analysis in asymmetric normed spaces, Springer, Basel, 2013.
  • Cosentino M. and Vetro P., Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat 28(4), (2014), 715--722.
  • Durmaz G., Mınak G. and Altun I., Fixed point results for α-ψ-contractive mappings including almost contractions and applications, Abst. Appl. Anal. 2014 (2014), 10 pages.
  • Gaba Y. U., Startpoints and (α-γ)-contractions in quasi-pseudometric spaces, J. Math. 2014 (2014), 8 pages.
  • Hussain N., Karapınar E., Salimi P. and Akbar F., α-admissible mappings and related fixed point theorems, J. Inequal. Appl. 2013 (2013), 11 pages.
  • Hussain N., Vetro C. and Vetro F., Fixed point results for α-implicit contractions with application to integral equations, Nonlinear Anal. Model. Control 21 (2016), 362--378.
  • Kelly, J. C., Bitopological spaces, Proc. London Math. Soc. 13 (1963), 71--89.
  • Künzi, H. P. A., Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology. In: Aull, CE, Lowen, R (eds.) Handbook of the History of General Topology, (3) (2001), 853--968.
  • Künzi H. P. A. and Vajner V., Weighted quasi-metrics, Ann. New York Acad. Sci. 728 (1994), 64--67.
  • Karapınar E. and Samet B., Generalized α-ψ-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012 (2012), 17 pages.
  • Kumam P., Vetro C. and Vetro F., Fixed points for weak α-ψ-contractions in partial metric spaces, Abstr. Appl. Anal. 2013 (2013), 9 pages.
  • Latif A. and Al-Mezel S. A., Fixed point results in quasimetric spaces, Fixed Point Theory Appl. 2011 (2011), 8 pages.
  • Mınak G., Helvacı A. and Altun I., Generalized Ciric type F-contractions on complete metric spaces and fixed point results, Filomat 28:6 (2014), 1143--1151.
  • Marin J., Romeguera S. and Tirado P., Weakly contractive multivalued maps and ω-distances on complete quasi-metric spaces, Fixed Point Theory Appl. 2011 (2011), 9 pages.
  • Marin, J., Romeguera, S. and Tirado, P., Generalized contractive set-valued maps on complete preordered quasi-metric spaces, J. Funct. Spaces Appl. 2013 (2013), 6 pages.
  • Reilly I. L., Subrahmanyam P. V. and Vamanamurthy M. K., Cauchy sequences in quasi- pseudo-metric spaces, Monatsh. Math. 93 (1982), 127--140.
  • Sgrio M. and Vetro C., Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat 27(7), (2013), 1259--1268.
  • Samet B., Vetro C. and Vetro P., Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154--2165.
  • Şimşek H. and Altun I., Two type quasi-contractions on quasi metric spaces and some fixed point results, J. Nonlinear Sci. Appl. 10 (2017), 3777--3783.
  • Wardowski D., Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012), 6 pp.
Year 2019, Volume: 68 Issue: 2, 1819 - 1830, 01.08.2019
https://doi.org/10.31801/cfsuasmas.419821

Abstract

References

  • Alemany E. and Romaguera, S., On half-completion and bicompletion of quasi-metric spaces, Comment. Math. Univ. Carolin. 37(4), (1996), 749--756.
  • Al-Homidan, S., Ansari, Q. H.and Yao, J. C., Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory, Nonlinear Anal. 69(1), (2008), 126--139.
  • Altun, I., Olgun M. and Mınak G., Classification of completeness of quasi metric space and some new fixed point results, Nonlinear Functional Analysis and Applications 22(2), (2017), 371--384.
  • Altun, I., Mınak G. and Dağ H., Multivalued F-contractions on complete metric space, J. Nonlinear Convex Anal. 16(4), (2015), 659--666.
  • Altun, I., Olgun M. and Mınak, G., A new approach to the Assad-Kirk fixed point theorem, J. Fixed Point Theory Appl. 18(1), (2016), 201--212.
  • Altun, I., Olgun M. and Mınak G., On a new class of multivalued weakly Picard operators on complete metric spaces, Taiwanese J. Math. 19(3), (2015), 659--672.
  • Ali M. U., Kamran T. and Shahzad N., Best proximity point for α-ψ-proximal contractive multimaps, Abstr. Appl. Anal. 2014 (2014), 6 pages.
  • Alegre C., Marin J. and Romeguera S., A fixed point theorem for generalized contractions involving ω-distances on complete quasi-metric spaces, Fixed Point Theory Appl. 2014 (2014), 8 pages.
  • Cobzaş, S., Completeness in quasi-metric spaces and Ekeland variational principle, Topology Appl. 158(2011), 1073--1084.
  • Cobzaş, S., Functional analysis in asymmetric normed spaces, Springer, Basel, 2013.
  • Cosentino M. and Vetro P., Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat 28(4), (2014), 715--722.
  • Durmaz G., Mınak G. and Altun I., Fixed point results for α-ψ-contractive mappings including almost contractions and applications, Abst. Appl. Anal. 2014 (2014), 10 pages.
  • Gaba Y. U., Startpoints and (α-γ)-contractions in quasi-pseudometric spaces, J. Math. 2014 (2014), 8 pages.
  • Hussain N., Karapınar E., Salimi P. and Akbar F., α-admissible mappings and related fixed point theorems, J. Inequal. Appl. 2013 (2013), 11 pages.
  • Hussain N., Vetro C. and Vetro F., Fixed point results for α-implicit contractions with application to integral equations, Nonlinear Anal. Model. Control 21 (2016), 362--378.
  • Kelly, J. C., Bitopological spaces, Proc. London Math. Soc. 13 (1963), 71--89.
  • Künzi, H. P. A., Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology. In: Aull, CE, Lowen, R (eds.) Handbook of the History of General Topology, (3) (2001), 853--968.
  • Künzi H. P. A. and Vajner V., Weighted quasi-metrics, Ann. New York Acad. Sci. 728 (1994), 64--67.
  • Karapınar E. and Samet B., Generalized α-ψ-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012 (2012), 17 pages.
  • Kumam P., Vetro C. and Vetro F., Fixed points for weak α-ψ-contractions in partial metric spaces, Abstr. Appl. Anal. 2013 (2013), 9 pages.
  • Latif A. and Al-Mezel S. A., Fixed point results in quasimetric spaces, Fixed Point Theory Appl. 2011 (2011), 8 pages.
  • Mınak G., Helvacı A. and Altun I., Generalized Ciric type F-contractions on complete metric spaces and fixed point results, Filomat 28:6 (2014), 1143--1151.
  • Marin J., Romeguera S. and Tirado P., Weakly contractive multivalued maps and ω-distances on complete quasi-metric spaces, Fixed Point Theory Appl. 2011 (2011), 9 pages.
  • Marin, J., Romeguera, S. and Tirado, P., Generalized contractive set-valued maps on complete preordered quasi-metric spaces, J. Funct. Spaces Appl. 2013 (2013), 6 pages.
  • Reilly I. L., Subrahmanyam P. V. and Vamanamurthy M. K., Cauchy sequences in quasi- pseudo-metric spaces, Monatsh. Math. 93 (1982), 127--140.
  • Sgrio M. and Vetro C., Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat 27(7), (2013), 1259--1268.
  • Samet B., Vetro C. and Vetro P., Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154--2165.
  • Şimşek H. and Altun I., Two type quasi-contractions on quasi metric spaces and some fixed point results, J. Nonlinear Sci. Appl. 10 (2017), 3777--3783.
  • Wardowski D., Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012), 6 pp.
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Hatice Aslan Hançer

Publication Date August 1, 2019
Submission Date April 30, 2018
Acceptance Date January 15, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Aslan Hançer, H. (2019). On two types almost (α,F_{d})-contractions on quasi metric space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1819-1830. https://doi.org/10.31801/cfsuasmas.419821
AMA Aslan Hançer H. On two types almost (α,F_{d})-contractions on quasi metric space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1819-1830. doi:10.31801/cfsuasmas.419821
Chicago Aslan Hançer, Hatice. “On Two Types Almost (α,F_{d})-Contractions on Quasi Metric Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1819-30. https://doi.org/10.31801/cfsuasmas.419821.
EndNote Aslan Hançer H (August 1, 2019) On two types almost (α,F_{d})-contractions on quasi metric space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1819–1830.
IEEE H. Aslan Hançer, “On two types almost (α,F_{d})-contractions on quasi metric space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1819–1830, 2019, doi: 10.31801/cfsuasmas.419821.
ISNAD Aslan Hançer, Hatice. “On Two Types Almost (α,F_{d})-Contractions on Quasi Metric Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1819-1830. https://doi.org/10.31801/cfsuasmas.419821.
JAMA Aslan Hançer H. On two types almost (α,F_{d})-contractions on quasi metric space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1819–1830.
MLA Aslan Hançer, Hatice. “On Two Types Almost (α,F_{d})-Contractions on Quasi Metric Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1819-30, doi:10.31801/cfsuasmas.419821.
Vancouver Aslan Hançer H. On two types almost (α,F_{d})-contractions on quasi metric space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1819-30.

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

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