Some New Results on Fixed Points for 𝜛-Distances in Complex-Valued Metric Spaces

Authors

  • Wongvisarut Khuangsatung Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathum Thani 12110, Thailand
  • Anteneh Getachew Gebrie Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan 445, Ethiopia
  • Cholatis Suanoom Program of Mathematics, Faculty of Science and Technology, Kamphaengphet Rajabhat University, Kamphaengphet 62000, Thailand

Keywords:

𝜛-distance, Ω-distance, 𝑐-distance, Complex-valued metric spaces, Fixed point, Generalized 𝑐-distance, 𝑤𝑡-distance, 𝑤-distance

Abstract

In this paper, we introduce the notion of a 𝜛-distance in complete complex-valued metric spaces and prove some fixed point theorems for mappings satisfying some appropriate inequalities in complete complex-valued metric spaces. Moreover, we deduce new fixed point results in complete complex-valued metric spaces and provide some examples to illustrate the usability of the obtained results.

References

S.Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1992) 133-181.

N.Artsawang, Accelerated preconditioning Krasnosel’ski’ı-Mann method for efficiently solving monotone inclusion problems , AIMS Mathematics, 8(12): (2023) 28398-28412. DOI: 10.3934/math.20231453

N.NIMANA1 and N.ARTSAWANG, A strongly convergent simultaneous cutter method for finding the minimal norm solution to common fixed point problem, CARPATHIAN J. MATH. Volume 40, No. 1, (2024) 155-171. DOI: https://doi.org/10.37193/CJM.2024.01.11

Z. Mustafa and B. Sims, Some remarks concerning D-metric spaces, Proceedings of the International Conference on Fixed Point Theory and Applications., (2004) 189-198, Valencia, Spain, July.

IA. Bakhtin, The contraction principle in quasimetric spaces, In: Functional Analysis., 30 (1989) 26-37.

M.H. Shah and N. Hussain Nonlinear contractions in partially ordered quasi b-metric spaces, In: Commun. Korean Math. Soc., 27(1) (2012) 117-128.

M.A. Alghamdi, N. Hussain and P.Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal., Appl., 402 (2013).

C. Klin-eam and C. Suanoom, Dislocated quasi-b-metric spaces and fixed point theorems for cyclic contractions, Fixed point theory and applications.,74 (2015). DOI 10.1186/s13663-015-0325-2

A.Azam, B.Fisher, M.Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim., 32 (3) (2011) 243-253.

S. Bhatt, S. Chaukiyal and R. C. Dimri, A common fixed point theorem for weakly compatible maps in complex-valued metric spaces, Int. J. Math. Sci. Appl., 1(2011) 1385-1389.

P. Kumam and W. Sintunavarat and, Generalized common fixed point theorems in complex valued metric spaces and applications, Journal of Inequalities and Applications., 84 (2012).

F. Rouzkard, M. Imdad, Some common fixed point theorems on complex valued metric spaces, Computers and Mathematics with Applications., 64 (2012) 186-1874.

C. Klin-eam and C. Suanoom, On complex valued -metric spaces and relafixed point theorems,International Journal of Nonlinear Analysis and Applications 12 (1), (2021) 748-760

C. Klin-eam and C.Suanoom , Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces, Abstract and Applied Analysis., 6 (2013).

C. Klin-Eam, J.Ahmad and A.zam , Common Fixed Points for Multivalued Mappings in Complex Valued Metric Spaces with Applications, Abstract and Applied Analysis., 12 (2013).

N. Hooda and Savitri A common coupled fixed point theorem in complex valued metric space, International Journal of Computer Applications., 109(4) (2015) 0975-8887.

O. Kada, T.Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japonica., 4 (1996) 381-391.

S. Wang and B. Guo, Distance in cone metric spaces and common fixed point theorems, Applied Mathematical Letters. 24 (2011) 1735-1739.

Z. M. Fadail and A. G. B. Ahmad, Coupled fixed point theorems of singlevalued mapping for c-distance in cone metric spaces, Journal of Applied Mathematics., 20 (2012).

Z. M. Fadail and A. G. B. Ahmad, Common coupled fixed point theorems of single-valued mapping for c-distance in cone metric spaces, Abstract and Applied Analysis., 24 (2012).

L. Gholizadeh, R. Saadati, W. Shatanawi, and SM. Vaezpour, Contractive mapping in generalized, ordered metric spaces with application in integral equations, Math. Probl. Eng., (2011.)

W. Shatanawi and A. Pitea, Fixed and coupled fixed point theorems of omegadistance for nonlinear contraction, Fixed Point Theory and Applications., 2 (75) (2013).

N. Hussain , R. Saadati and R.P. Agrawal , On the topology and wt-distance on metric type spaces, Fixed Point Theory and Applications., 88(14) (2014).

S. K. Mohanta, Some fixed point theorems using wt-distance in b-metric spaces, AMS Mathematics Subject Classification., 54 (2015).

B. Bao, S. Xu, L. Shi and V. C. Rajic, Fixed point theorems on generalized cdistance in ordered cone b-metric spaces, Int. J. Nonlinear Anal. Appl., 6(1) (2015) 9-22.

Z. M. Fadail and A.G.B. Ahmad, Generalized c-distance in cone b-metric spaces and common fixed point results for weakly compatible self mappings, International Journal of Mathematical Analysis., 9(32) (2015) 1593-1607

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Published

2024-06-25

How to Cite

Khuangsatung, W. ., Gebrie, A. G. ., & Suanoom, C. (2024). Some New Results on Fixed Points for 𝜛-Distances in Complex-Valued Metric Spaces. Science & Technology Asia, 29(2), 173–182. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/252461

Issue

Vol.29 No.2 (April-June 2024)

Section

Physical sciences

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