Algorithmic and analytical approach to the proximal split feasibility problem and fixed point problem

Abstract

In this paper, we investigate the proximal split feasibility algorithm and fixed point problem in Hilbert spaces. We propose an iterative algorithm for finding a common element of the solution of the proximal split feasibility algorithm and fixed point of an L-Lipschitz pseudocontractive operator. We demonstrate that the considered algorithm converges strongly to a common point of the investigated problems under some mild conditions.

A Novel Investigation of Non-Periodic Snap BVP in the G-Caputo Sense

“…exist and are continuous. Hence, by applying the δ-th integral I δ;G τ + 1 to both sides of Equation (10), by Lemma 2, we obtain…”

“…Many researchers have investigated the sufficient conditions for a wide domain of fractional nonlinear ordinary differential equations by employing methods which include standard fixed-point theorems, iterative approaches, etc. (see [5][6][7][8][9][10][11][12][13]). However, to the best of our knowledge, limited results can be found on the existence/stability of solutions for a fractional jerk system via the generalized G-Caputo derivative.…”