## Fixed point results of generalized $\alpha-\left( {\psi ,\phi } \right)-Z_G-$ contractive mappings on non-Archimedean modular metric spaces -by Ekber Girgin and Mahpeyker Ozturk

Abstract: In this paper, by using the concept of $\alpha$-admissible mapping and generalized class of simulation functions, we establish the existence and uniqueness of fixed point of a generalized $\alpha- \left( {\psi ,\phi } \right) - Z_G-$ contractive mappings on non-Archimedean modular metric spaces. Our results generalize and extend various comparable results in the…

## A novel iteration algorithm for a hybrid pair of total asymptotically non-expansive single-valued and total asymptotically quasi-non-expansive multi-valued non-self mappings in Banach spaces -by Imo Kalu Agwu

Abstract: In this paper, we introduce a new mixed-type iteration scheme for finite family of total asymptotically nonexpansive single-valued and finite family of total asymptotically quasi-nonexpansive multi-valued nonself mappings. In addition, we prove weak and strong convergence theorems of the proposed iteration algorithm in Banach spaces. Our main results were obtained without any strict condition…

## A damped algorithm for minimum-norm solution of the proximal split feasibility problem -by Caifen Zhang and Jinzuo Chen

Abstract: The aim of the paper is to introduce an iterative algorithm for finding the least norm solution of the proximal split feasibility problem. We present a damped algorithm from which strong convergence theorem is obtained in Hilbert spaces. We apply this algorithm to solve split equilibrium problem. Numerical example is included. Keywords: Proximal split feasibility…

## Existence and stability results for stochastic functional integro-differential equations with poisson jumps under non-Lipschitz conditions -by A. Anguraj, K. Ravikumar and K. Ramkumar

Abstract: In this paper, we investigate the existence results on averaging principle and stability of mild solutions for stochastic functional integro-differential equations with poisson jumps under non-Lipschitz condition. We establish the results by the method of successive approximation and Bihari’s inequality under the theory of resolvent operators. Keywords: Existence, Uniqueness, Stability, Averaging principle, Bihari’s inequality,…

## The existence and uniqueness of $\varphi-$Best proximity point theorems for generalized Boyd-Wong proximal contraction -by Urairat Deepan and Poom Kumam

Abstract: In this paper, we study concept and expand the condition of I\c{s}ik, Sezen and Vetro [1] to prove the existence and uniqueness of $\varphi-$best proximity point for $(F,\lambda,\varphi)-$weak proximal and $(F,\lambda,\varphi)-$proximal contraction. As for applications of our main results, we prove the existence and uniqueness of a fixed point on partial metric spaces and…

## Layered Monotonic Fixed Point Theorem -by Richard I. Avery, Douglas R. Anderson and Johnny Henderson

Abstract: In this paper, we decompose an operator as the sum of an increasing operator and a decreasing operator, with a condition that the change in the increasing component is greater than the change in the decreasing component on a given set, which allows us to use a monotonic iterative method to find a fixed…