In this presented book contains six chapters that areIntroduction, Review of Literature, Random Fixed point theorems and application in Sb metric spaces, Perov Type Results in Gauge Spaces and its Applications to Systems of Integral Equations, Hyers Ulam Stability And Solutions For A Class Of Nonlinear Integral Equations By Fixed Point Technique, Fixed point theorems for the sum of three classes of mixed monotone operators and applications, Tripled Common fixed point results in ordered S-metric spaces. We prove some random fixed point theorems and apply our obtained results to show existence of a unique solution to an initial value problem as an application. We also prove a tripled coincidence and common fixed point theorems for commuting mappings with mixed g-monotone property in partially ordered S-metric spaces. Our obtained results are applied for solving nonlinear fractional differential equations with integral boundary conditions, and also, we give some specific examples.