Some generalizations for mixed multivalued mappings

Mustafa Aslantaş; Hakan Sahin; Uğur Sadullah

doi:10.4995/agt.2022.15214

Authors

Mustafa Aslantaş Çankırı Karatekin University https://orcid.org/0000-0003-4338-3518
Hakan Sahin Amasya University https://orcid.org/0000-0002-4671-7950
Uğur Sadullah Çankırı Karatekin University https://orcid.org/0000-0001-8463-2862

DOI:

https://doi.org/10.4995/agt.2022.15214

Keywords:

fixed point, mixed multivalued mapping, M-metric space, Pompeiu-Hausdorff metric

Abstract

In this paper, we first introduce a new concept of KW-type m-contraction mapping. Then, we obtain some fixed point results for these mappings on M-metric spaces. Thus, we extend many well-known results for both single valued mappings and multivalued mappings such as the main results of Klim and Wardowski [13] and Altun et al. [4]. Also, we provide an interesting example to show the effectiveness of our result.

Downloads

Download data is not yet available.

Author Biographies

Mustafa Aslantaş, Çankırı Karatekin University

Department of Mathematics, Faculty of Science

Hakan Sahin, Amasya University

Department of Mathematics, Faculty of Science and Arts

Uğur Sadullah, Çankırı Karatekin University

Department of Mathematics, Faculty of Science

References

M. Abbas and T. Nazir, Fixed point of generalized weakly contractive mappings in ordered partial metric spaces, Fixed Point Theory and Applications 2012, no. 1 (2012), 1-19. https://doi.org/10.1186/1687-1812-2012-1

N. Alamgir, Q. Kiran, H. Aydi and Y. U. Gaba, Fuzzy fixed point results of generalized almost F-contractions in controlled metric spaces, Adv. Differ. Equ. 2021 (2021): 476. https://doi.org/10.1186/s13662-021-03598-0

I. Altun, H. Sahin and D. Turkoglu, Caristi-type fixed point theorems and some generalizations on M-metric space, Bul. Mal. Math. Sci. Soc. 43, no. 3 (2020), 2647-2657. https://doi.org/10.1007/s40840-019-00823-8

I. Altun, H. Sahin and D. Turkoglu, Fixed point results for multivalued mappings of Feng-Liu type on M-metric spaces, J. Non. Funct. Anal. 2018 (2018), 1-8. https://doi.org/10.23952/jnfa.2018.7

I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. 157, no. 18 (2010), 2778-2785. https://doi.org/10.1016/j.topol.2010.08.017

M. Asadi, E. Karapınar and P. Salimi, New extension of p-metric spaces with some fixed point results on M-metric spaces, J. Ine. Appl. 2014 (2014), 18. https://doi.org/10.1186/1029-242X-2014-18

S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181

L. Ćirić, B. Samet, H. Aydi and C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, App. Math. and Comp. 218, no. 6 (2011), 2398-2406. https://doi.org/10.1016/j.amc.2011.07.005

Y. Feng and S. Liu, Fixed point theorems for multi-valued contractive mappings and multivalued Caristi type mappings, J. Math. Anal. Appl. 317 (2006), 103-112. https://doi.org/10.1016/j.jmaa.2005.12.004

Y. U. Gaba, M. Aphane and V. Sihag, On two Banach-type fixed points in bipolar metric spaces, Abstract and Applied Analysis 2021 (2021), 1-10. https://doi.org/10.1155/2021/4846877

Y. U. Gaba and E. Karapınar, A new approach to the interpolative contractions, Axioms 8, no. 4 (2019): 110. https://doi.org/10.3390/axioms8040110

Z. Kadelburg and S. Radenovic, Fixed point and tripled fixed point theorems under Pata-type conditions in ordered metric spaces, Inter. J. of Anal. and Appl. 6 (2014), 113-122. [23]

D. Klim and D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334, no. 1 (2007), 132-139. https://doi.org/10.1016/j.jmaa.2006.12.012

S. G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences-Paper Edition 728 (1994), 183-197. https://doi.org/10.1111/j.1749-6632.1994.tb44144.x

N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141, no. 1 (1989), 177-188. https://doi.org/10.1016/0022-247X(89)90214-X

N. Mlaiki, K. Abodayeh, H. Aydi, T. Abdeljawad and M. Abuloha, Rectangular metric-like type spaces and related fixed points, Journal of Mathematics 2018 (2018), 1-8. https://doi.org/10.1155/2018/3581768

S. B. Nadler, Multi-valued contraction mappings, Pacific Journal of Mathematics 30, no. 2 (1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475

N. Y. Özgür, N. Mlaiki, N. Taş and N. Souayah, A new generalization of metric spaces: rectangular M-metric spaces, Mathematical Sciences 12, no. 3 (2018), 223-233. https://doi.org/10.1007/s40096-018-0262-4

S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital. 5 (1972), 26-42. [40]

S. Reich, Some problems and results in fixed point theory, Contemp. Math. 21 (1983), 179-187. https://doi.org/10.1090/conm/021/729515

S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory and Applications 2010 (2009): 493298. https://doi.org/10.1155/2010/493298

S. Romaguera, On Nadler's fixed point theorem for partial metric spaces, Mathematical Sciences and Applications E-Notes 1, no. 1 (2013), 1-8.