TY - JOUR
ID - 4491
TI - On some fixed point results for $(alpha, beta)$-Berinde-$varphi$-Contraction mapppings with applications
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Mebawondu, Akindele
AU - Izuchukwu, Chinedu
AU - Aremu, Kazeem
AU - Mewomo, Oluwatosin Temitope
AD - School of Mathematics, Statistics and Computer Science, University of KwaZulu-
Natal, Durban, South Africa
Y1 - 2020
PY - 2020
VL - 11
IS - 2
SP - 363
EP - 378
KW - $(alpha, beta)$-cyclic admissible mapping
KW - $(alpha, beta)$-Berinde-$varphi$-contraction mapping
KW - Fixed point
KW - metric space
DO - 10.22075/ijnaa.2020.20635.2183
N2 - The aim of this paper is to introduce a new class of mappings called $(alpha, beta)$-Berinde-$varphi$-contraction mappings and to establish some fixed point results for this class of mappings in the frame work of metric spaces. Furthermore, we applied our results to the existence of solution of second order differential equations and the existence of a solution for the following nonlinear integral equation: begin{align*} x(t)=g(t)+int_a^bM(t,s)K(t,x(s))ds, end{align*} where $M:[a,b]times [a,b]tomathbb{R}^+,$ $K:[a,b]times mathbb{R}to mathbb{R}$ and $ g:[a,b]to mathbb{R}$ are continuous functions. Our results improve, extend and generalize some known results in the literature. In particular, our main result is a generalization of the fixed point result of Pant cite{ran}.
UR - https://ijnaa.semnan.ac.ir/article_4491.html
L1 - https://ijnaa.semnan.ac.ir/article_4491_75a0c78d4122489ab92f56eb7b478bbf.pdf
ER -