Some Fixed Point Theorems on $b$-$\theta$-metric spaces via $b$-simulation Functions

Year 2021, Volume: 4 Issue: 3, 159 - 164, 30.09.2021

Esra Dalan Yıldırım Ayşegül Çaksu Güler Oya Bedre Özbakır

https://doi.org/10.33401/fujma.890533

Abstract

We introduce the concept of $b$-$\theta$-metric space as a generalization of $\theta$-metric space and investigate some of its properties. Then, we establish a fixed point theorem in $b$-$\theta$-metric spaces via $b$-simulation functions. Thus, we deduce Banach type fixed point in such spaces. Also, we discuss some fixed point results in relation to existing ones.

Keywords

b-metric, b-simulation function, $\theta$-metric, b-$\theta$-metric

References

• [1] I. A. Bakhtin, The contraction mapping principle in almost metric space, Functional Analysis, 30(1989), 26-37.
• [2] S. Czerwik, Contraction mappings in b-metric spaces, Acta. Math. Inform. Univ. Ostraviensis, 1(1993), 5-11.
• [3] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46(1998), 263-276.
• [4] R. George, B. Fisher, Some generalized results of fixed points in cone b-metric spaces, Math. Moravic., 17(2013), 39- 50.
• [5] F. Khojasteh, E. Karapinar, S. Randenvic, q-metric space: a generalization, Math. Probl. Eng., Art. ID:504609, (2013), 7pp.
• [6] F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat, 29(6)(2015), 1189- 1194.
• [7] A.Chanda, B. Damjanovi ´ c, L. K. Dey, Fixed point results on q-metric spaces via simulation functions, Filomat, 31(11)(2017), 3365-3375.
• [8] M. Demma, R. Saadati, P. Vetro, Fixed point results on b-metric space via Picard sequences and b- simulation functions, Iranian J. Math. Sci. Inform., 11(1)(2016), 123- 136.