A study of coincidence point theorems for multivalued mappings on extended $m_b$-metric spaces

Patra, Shilpa

doi:10.30495/maca.2025.2060635.1137

A study of coincidence point theorems for multivalued mappings on extended $m_b$-metric spaces

10.30495/maca.2025.2060635.1137

Volume 7, Issue 3
Summer 2025

Pages 127-140

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Author

Shilpa Patra

Department of Mathematics, Narajole Raj College, Paschim Medinipur, West Bengal, India

Abstract

In recent studies, the exploration of coincidence points represents a fresh development within the area of contractive-type single-valued and multivalued theory. This paper establishes new coincidence point theorems pertaining to both single-valued and multivalued mappings within the context of extended $m_b$-metric spaces. Employing methodologies derived from classical fixed point theorems, such as Banach’s Contraction Principle and Kannan’s fixed point results, we elucidate the requisite conditions under which these mappings exhibit coincidence points. To underscore the practical implications of our principal theorem, we present an illustrative example that validates the results. These contributions advance the understanding of fixed point theory in extended $m_b$-metric spaces and offer new avenues for further research in this area.

Keywords

Extended mb-metric space

multivalued mapping

$H_\theta$-contraction

coincidence point

[1] K. Abodayeh, N. Mlaiki, T. Abdeljawad, and W. Shatanawi, Relations between partial metric spaces and M-metric spaces, Caristi Kirk’s theorem in M-metric type spaces, J. Math. Anal., 7(3) (2016), 1–12.

[2] S. M. A. Aleomraninejad, Sh. Rezapour, and N. Shahzad, Convergence of an iterative scheme for multifunctions, J. Fixed Point Theory Appl., 12 (2012), 239–246.

[3] S. M. A. Aleomraninejad and N. Shahzad, On fixed point generalizations of Suzuki’s method, Appl. Math. Lett., 24 (2011), 1037–1040.

[4] M. Asadi, E. Karapinar, and P. Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. Inequal. Appl., 2014 (2014), 1–9.

[5] I. Beg, and A. Azam, Fixed points of multivalued locally contractive mappings, Boll. Unione Mate. Ital., 7 (1990), 227–233.

[6] I. Beg, and A. R. Butt, Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal.: Theory Meth. Appl., 71 (2009), 3699–3704.

[7] B. Damjanovic, B. Samet, and C. Vetro, Common fixed point theorems for multi-valued maps, Acta Math. Sci. Ser. B Engl. Ed., 32 (2012), 818–824.

[8] S. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci., 728 (1994), 183-197.

[9] N. Mlaiki, N. Ozgur, N. Y. Mukheimer, and A. N. Tas, A new extension of the Mb-metric spaces, J. Math. Anal., 9(2) (2018), 118–133.

[10] S. Mohanta, and S. Patra, Coincidence Point Results for Different Types of H⁺_b-contractions on mb-Metric Spaces, Sahand Commun. Math. Anal., 18(2) (2021), 1–31.

[11] H. Monfared, M. Azhini, and M. Asadi, Fixed point results in M-metric spaces, J. Math. Anal., 7(5) (2016), 85–101.

[12] S. B. Nadler, Multivalued contraction mappings, Pacific J. Math., 30 (1969), 475–488.

[13] H. Sahin, I. Altun and D. Turkoglu, Fixed point results for mixed multivalued mappings of Feng-Liu type on Mb-metric spaces, Math. Meth. Engin. Nonlinear Syst. Complexity, 23 (2019), 67–80.

[14] W. Shatanawi, Fixed and common fixed point for mappings satisfying some nonlinear contractions in b-metric spaces, J. Mat. Anal., 7(4) (2016), 1–12.

XML

PDF 431.65 K