Developments of some new results that weaken certain conditions of fractional type differential equations

Abstract

We introduce double and triple F-expanding mappings. We prove related fixed point theorems. Based on our obtained results, we also prove the existence of a solution for fractional type differential equations by using a weaker condition than the sufficient small Lipschitz constant studied by Mehmood and Ahmad (AIMS Math. 5:385–398, 2019) and Hanadi et al. (Mathematics 8:1168, 2020). As applications, we ensure the existence of a unique solution of a boundary value problem for a second-order differential equation.

Fixed-Point Approximation of Operators Satisfying (RCSC)—Condition in CAT(0) Spaces

“…Some of these iteration processes are in Maan [4], Ishikawa [5], Agarwal et al [6], Thakur [7], Noor [8] and Abbas [9]. For more details on iteration processes, see [10][11][12][13][14][15][16][17] and references therein.…”