TY - JOUR
ID - 29263
TI - Rational Geraghty Contractive Mappings and Fixed Point Theorems in Ordered $b_2$-metric Spaces
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Jalal Shahkoohi, Roghaye
AU - Bagheri, Zohreh
AD - Department of Mathematics, Aliabad katoul Branch, Islamic Azad University, Aliabad katoul, Iran.
AD - Department of Mathematics, Azadshahr Branch, Islamic Azad University, Azadshahr, Iran.
Y1 - 2019
PY - 2019
VL - 13
IS - 1
SP - 179
EP - 212
KW - Fixed point
KW - Complete metric space
KW - Ordered $b_2$-metric space
DO - 10.22130/scma.2017.29263
N2 - In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces. These include Geraghty-type conditions, conditions that use comparison functions and almost generalized weakly contractive conditions. Berinde in [17-20] initiated the concept of almost contractions and obtained many interesting fixed point theorems. Results with similar conditions were obtained, \textit{e.g.}, in [21] and [22]. In the last section of the paper, we define the notion of almost generalized $(\psi ,\varphi )_{s,a}$-contractive mappings and prove some new results. In particular, we extend Theorems 2.1, 2.2 and 2.3 of Ciric et.al. in [23] to the setting of $b_{2}$-metric spaces. Also, some examples are provided to illustrate the results presented herein and several interesting consequences of our theorems are also provided. The findings of the paper are based on generalization and modification of some recently reported theorems in the literature.
UR - https://scma.maragheh.ac.ir/article_29263.html
L1 - https://scma.maragheh.ac.ir/article_29263_f6da7913f6ba4c54cf195c5e7a308a31.pdf
ER -