Fixed Point Theorems for Mizoguchi-Takahashi Type Contraction in Bicomplex-Valued Metric Spaces and Applications

Abstract

The main aim of this paper is to study and establish some new fixed point theorems for contractive maps that satisfied Mizoguchi-Takahashi’s condition in the setting of bicomplex-valued metric spaces. These new results improve and generalize the Banach contraction principle and some well-known results in the literature. Finally, as applications of our results, we give the existence and uniqueness of the solution of a nonlinear integral equation.

Riemann–Liouville fractional operators of bicomplex order and its properties

“…The bicomplex finite element method that can be applied for wave propagation problems in various environments was presented by Reum and Toepfer 23 . A necessary and sufficient condition for the general principle of convergence of infinite product of bicomplex number, some of its consequences, and validity of the theorems were given in Dutta et al 24 Work has been done on some new fixed point theorems for contractive maps that satisfied Mizoguchi–Takahashi's condition in the setting of bicomplex‐valued metric spaces with existence and uniqueness of the solution of a nonlinear integral equation 25 . Kobayashi 26 introduced twin‐multistate activation functions to reduce the number of weight parameters and discussed bicomplex‐valued twin‐multistate Hopfield neural network (BTMHNN) to improve the noise tolerance.…”