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Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Fixed point theorems for (z, a, b)-contraction

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pp. 1923–1932Vol. 27Issue 8December 2024DOI: 10.47974/JIM-2059XML
Received:
10 Jul 2024
Published Online:
16 Dec 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-2059
Pages:
1923–1932

Abstract

This project aims to introduce (z, a, b)-contractions of type-A in b-metric-like spaces (BMLS) utilizing (a, b)-Geraghty contractions [9] introduced in 2019. In the first section of this work, a new class Yp is defined as a collection of maps with certain appropriate constraints. Then, using this class z : [0, ∞)p → [0, ∞), some fixed point findings are presented with an illustration for efficacy check. Many results in the literature are supported by our findings.

Keywords

Subject Classifications

47H1054H25

References

[1] A. Meir and E. Keeler, “A thorem on contractive mappings”, Journal of Mathematical Analysis and applications, vol. 281, pp. 326-329 (1969). 
[2] B. Samet, C. Vetro and P. Vetro, “Fixed point theorems for -contractive type mappings”, Nonlinear Analysis: Theory, Methods and Applications, vol. 75, no. 4, pp. 2154-2165 (2012). 
[3] B. E. Rhoades, “Some theorems on weakly contractive maps”, Nonlinear Analysis: Theory, Methods & Applications, vol. 47, pp. 2683-2694 (2001). 
[4] C. B. Nadler, “Multivalued contraction mappings”, Pacific Journal of Mathematics, vol. 30, pp. 475-488 (1969). 
[5] D. Wardowski, “Fixed points of a new type of contractive mappings in complete metric spaces,” Fixed Point Theory and Applications, vol. 2012, no. 94 (2012).
[6] L. B. Ciric, “A generalization of Banachs contraction principle”,  Proceeding of the American Mathematical Society, vol. 45, pp. 267-273 (1974). 
[7] M. A. Alghamdi, N. Hussain, and P. Salimi, “Fixed point and coupled fixed point theorems on b-metric like spaces,” Journal of Inequalities and Applications, vol. 2013, no. 402 (2013).
[8] M. D. Sen, N. Nicolic, T. Dosenovic, M. Pavlovic and S. Radenovic, “Some Results on (s-q)-Graphic Contraction Mapping in b-Metric-like Spaces”, Mathematics, vol. 7, no. 12. pp. 1190 (2019). 
[9] N. Mlaiki, N. Dedovic, H. Aydi, M. G. Filipovic, B. B. Mohsin and S. Radenovic, “Some new observations on Geraghty and Ciric type results in b-metric spaces”, Mathematics, vol. 7, no, 7, pp. 643 (2019).
[10] R. Kannan, “Some results on fixed points-II”, The American Mathematical Monthly, vol. 76, no. 4 pp. 405-408 (1969).
[11] R. Pant and R. Panicker, “Geraghty and Ciric type fixed point theorems in b-metric spaces”, Journal of Nonlinear Science and Applications, vol. 9, pp.  5741-5755  (2016).
[12] S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations integrals”. Fundamenta Mathematicae, vol. 3, pp. 133-181 (1922).
[13] S. Chandok, “Some fixed point theorems for (alpha,beta)-admissible Geraghty type contractive mappings and related results”, Mathematical Sciences, vol. 9, pp. 127-135 (2015).
[14] S. Czerwik, “Nonlinear set-valued contraction mapping in b-metric spaces”. Atti del Seminaro Matematico e Fisico dell’Universita di Modena e Reeggio Emilia, vol. 46, pp. 263-276 (1998).

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