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We introduce a large class of contractive mappings, called Suzuki–Berinde type contraction. We show that any Suzuki–Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mappings is also obtained. These results unify, generalize and complement various known comparable results in the literature. [ABSTRACT FROM AUTHOR]

Using a dynamical step size technique, a new self-adaptive CQ-algorithm is proposed in the presence of an inertial term to find the solution of convex feasibility problem and monotone inclusion problem involving a finite number of maximal monotone set valued operators. To do this, in certain Banach spaces, we construct an algorithm which converges to the fixed point of right Bregman strongly nonexpansive mappings and coincidentally solves the convex feasibility and monotone inclusion problems. Strong convergence of the algorithm is achieved without computation of the associated operator norms. Interesting numerical examples which illustrate the implementation and efficiency of our scheme are also given. Results obtained via this work improve and extend on previous results of its kind, in the literature. [ABSTRACT FROM AUTHOR]

In this study, we propose an inertial extragradient algorithm for solving a split generalized equilibrium problem as well as a split feasibility and common fixed point problem. We demonstrate that, under certain reasonable assumptions, the sequences induced by the proposed algorithm converge strongly to a solution of the corresponding problem. In addition, with the help of a numerical example, we demonstrate the efficiency of proposed algorithm. As a result of this paper, some recent well-known results in this area have been improved, generalized, and extended. [ABSTRACT FROM AUTHOR]

In this paper, we propose two inertial accelerated algorithms which do not require prior knowledge of operator norm for solving split feasibility problem with multiple output sets in real Hilbert spaces. We prove weak and strong convergence results for approximating the solution of the considered problem under certain mild conditions. We also give some numerical examples to demonstrate the performance and efficiency of our proposed algorithms over some existing related algorithms in the literature. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new kind of split monotone variational inclusion problem involving Cayley operator in the setting of infinite-dimensional Hilbert spaces. We develop a general iterative method to approximate the solution of the split monotone variational inclusion problem involving Cayley operator. Under some suitable conditions, a convergence theorem for the sequences generated by the proposed iterative scheme is established, which also solves certain variational inequality problems related to strongly positive linear operators. Finally, a numerical example is presented to study the efficiency of the proposed algorithm through MATLAB programming. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces. [ABSTRACT FROM AUTHOR]

The aim of this work is to establish fixed point theorems under rational type contractions in the framework of complex-valued metric spaces. These theorems extend and generalize some prominent results in the present literature. Furthermore, as an application the existence result is given for the system of Volterra–Hammerstein non-linear integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the class of asymptotically demicontractive multivalued mappings and establish a strong convergence theorem of the modified Mann iteration to a common fixed point of a finite family of asymptotically demicontractive multivalued mappings in a complete CAT(0) space. We also give a numerical example of our iterative method to show its applicability. [ABSTRACT FROM AUTHOR]

A mapping such that and is called a noncyclic mapping, where A and B are two nonempty subsets of a Banach space X. A best proximity pair for such a mapping T is a point such that and . In the current paper, we establish some existence results of best proximity pairs in strictly convex Banach spaces. The presented theorems improve and extend some recent results in the literature. We also obtain a generalized version of Markov-Kakutani's theorem for best proximity pairs in a strictly convex Banach space setting. [ABSTRACT FROM AUTHOR]

A general common fixed point theorem for two pairs of weakly subsequentially continuous mappings (recently introduced) satisfying a significant estimated implicit function is proved. An extension of this result is thereby obtained. Our results assert the existence and uniqueness of common fixed points in several cases. [ABSTRACT FROM AUTHOR]

In this paper, we propose a one-step iteration for the approximation of common fixed points of two uniformly continuous total asymptotically quasi-nonexpansive mappings in uniformly convex hyperbolic spaces. We establish strong convergence and Δ-convergence results of the proposed iteration in this setting. As a consequence, our convergence results improve and generalize various results announced in the current literature. [ABSTRACT FROM AUTHOR]