Common fixed point theorems under Pata’s contraction in complex valued metric spaces and an application to integral equations

Solving Integral Equations via Fixed Point Results Involving Rational-Type Inequalities

“…Furthermore, Azam et al [11] introduced the concept of metric spaces in the complex version in 2011 and Rao and their coauthors introduced the concept of b-metric spaces in the complex plane in 2013 [12]. Different fixed point results for mappings satisfying conditions of different types of contractions in complex and complex b-metric spaces have been justified and studied [13][14][15][16][17][18]. Although the concept of a complex-valued b-metric space is more general than that of a complex-valued metric space, both have been extensively studied in the literature.…”

Unique Common Fixed Point Result for Rational Contraction in Complex valued Metric Space

“…He created unique common fixed point results for pair of compatible mappings satisfying a rational inequality. Very much inventor have established several results of fixed points for various mappings satisfying a rational contraction in the context of the complex valued metric spaces, see for [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The purpose of this paper is to build up the common fixed point result for two sets of compatible mappings satisfying rational contraction in a complex valued metric space and we acquire the presence and uniqueness of a common solution for the arrangement of Urysohn integral equation.…”