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In this research, we offer a new proximal point technique for approximating a common member of the set of all solutions of the convex minimization problems in the setting of CAT(1) spaces. We further show that, in some modest circumstances, the resulting process is convergent. Our results extend and enhance other related results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the split common fixed point problem in Hilbert spaces. We find a common solution of the split common fixed point problem for two demicontractive operators without a priori knowledge of operator norms. A strong convergence theorem is obtained under some additional conditions and numerical examples are included to illustrate the applications in signal compressed sensing and image restoration.

In this paper, we explore the existence and uniqueness of fixed points for the new constructed contraction mapping on dislocated quasi-metric spaces by using Geraghty contraction and F-contraction. Moreover, we support our results by a couple of non-trivial examples. [ABSTRACT FROM AUTHOR]

In this article, we offer two modifications of the modified forward‐backward splitting method based on inertial Tseng method and viscosity method for inclusion problems in real Hilbert spaces. Under standard assumptions, such as Lipschitz continuity and monotonicity (also maximal monotonicity), we establish weak and strong convergence of the proposed algorithms. We give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for solving the image deblurring and image recovery problems. Our result extends some related works in the literature and the primary experiments might also suggest their potential applicability. [ABSTRACT FROM AUTHOR]

In this paper, we present some results on the existence of coincidence and periodic point of F-contractive mappings in the framework of modular metric spaces endowed with a graph. We also present an application to partial differential equations in order to support the theoretical results. [ABSTRACT FROM AUTHOR]

In paper, we prove some common fixed point theorems for the pair of self-mappings with the g-quasi-condition in modular metric spaces. Also, we modify and prove some common fixed point theorems by using the (CLRg)-property along with the weakly compatible mapping. Finally, we give some applications on integral equations to illustrate our main results. [ABSTRACT FROM AUTHOR]