A new approximation scheme for solving various split inverse problems

A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces

“…This class of monotone mapping have been widely studied in literature (see [44,45]) for more details. If A is a monotone operator, then we can define, for each r > 0, a nonexpansive single-valued mapping J A r : R(I + rA) → D(A) by J A r := (I + rA) −1 which is generally known as the resolvent of A, (see [46,47]). It is also known that A −1 (0) = F(J A r ), where A −1 (0) = {x ∈ H : 0 ∈ Ax} and F(J A r ) = {x ∈ H :…”

An inertial method for a solution of split equality of monotone inclusion and the f$$ f $$‐fixed point problems in Banach spaces

“…Motivated and inspired by the works of Moudafi, 9 Taiwo et al, 10,24 Izuchukwu et al, 12 and Sunthrayuth et al, 26 we introduce and study an inertial algorithm, which converges strongly to a solution of split equality of monotone inclusion and $$$ f,g $$$‐fixed point of Bregman relatively $$$ f,g $$$‐nonexpansive mapping problems () in reflexive real Banach spaces. In addition, we provide several applications of our method and provide a numerical example to demonstrate the behavior of the convergence of the algorithm to a solution of the indicated problems.…”

“…The split monotone inclusion and fixed point problem (SMIFPP) 10 is the generalization of SMIP, which is defined as finding a point $$$ \left(p,q\right)\in {H}_1\times {H}_2 $$$ such that $$$$ p\in F(T)\cap {\left(A+B\right)}^{-1}0,q\in F(G)\cap {\left(C+D\right)}^{-1}0\kern0.3em \mathrm{and}\kern0.3em S(p)=K(q), $$$$ where $$$ A:{H}_1\to {H}_1 $$$ and $$$ C:{H}_2\to {H}_2 $$$ are inverse strongly monotone mappings, $$$ B:{H}_1\to {2}^{H_1} $$$ and $$$ D:{H}_2\to {2}^{H_2} $$$ are maximal monotone mappings, $$$ T:{H}_1\to {H}_1 $$$ and $$$ G:{H}_2\to {H}_2 $$$ are demi‐contractive mappings, …”

A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

“…authors have studied and proposed many iterative algorithms for approximating the solution of variational inequality problem and related optimization problems, (see [10,20,26,25,29,44,46,49]) and the references therein. The variational inequality problem is widely known to be equivalent to the following fixed point equation:…”