# Fixed point integral equation sheet

The proof relies on transforming the differential equation, and applying fixed-point theory. By integrating both sides, any function satisfying the differential equation must also satisfy the integral equation − = ∫ (, ()). T1 - A common fixed point theorem and its application to nonlinear integral equations. AU - Pathak, H. K. AU - Khan, M. S. AU - Tiwari, Rakesh. PY - 2007/3. Y1 - 2007/3. N2 - In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings. Fixed Point Theorems for Manageable Contractions with Application to Integral Equations ... contraction and prove certain fixed point results. We also SOLUTION OF A FRACTIONAL ORDER INTEGRAL EQUATION VIA FIXED POINT THEOREM IN PSEUDOMODULAR METRIC SPACE Muhammad Usman Ali1, Tayyab Kamran2, Wisam Kassab3 An existence theorem for a class of fractional order integral equations is estab-lished in pseudomodular metric spaces. For this purpose, we rst introduce the notion Denoting the unknown function by φwe consider linear integral equations which involve an integral of the form K(x,s)φ(s)ds or K(x,s)φ(s)ds a x ∫ a b ∫ The type with integration over a fixed interval is called a Fredholm equation, while if the upper limit is x, a variable, it is a Volterra equation. The other fundamental division of these ... Aug 05, 2019 · A parabola is the locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to its distance from a fixed straight line in the same plane. If focus of a parabola is S(x 1 , y 1 ) and equation of the directrix is ax + by + c = 0, then the equation of the parabola is