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In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a class of new general iteration processes for two finite families of total asymptotically nonexpansive mappings in hyperbolic spaces, which includes asymptotically nonexpansive mapping, (generalized) nonexpansive mapping of all normed linear spaces, Hadamard manifolds and CAT(0) spaces as special cases. Some important related properties to the new general iterative processes are also given and analyzed, and Δ-convergence and strong convergence of the iteration in hyperbolic spaces are proved. Furthermore, some meaningful illustrations for clarifying our results and two open questions are proposed. The results presented in this paper extend and improve the corresponding results announced in the current literature. [ABSTRACT FROM AUTHOR]

We provide the semilocal convergence analysis of the Newton-Secant solver with a decomposition of a nonlinear operator under classical Lipschitz conditions for the first order Fréchet derivative and divided differences. We have weakened the sufficient convergence criteria, and obtained tighter error estimates. We give numerical experiments that confirm theoretical results. The same technique without additional conditions can be used to extend the applicability of other iterative solvers using inverses of linear operators. The novelty of the paper is that the improved results are obtained using parameters which are special cases of the ones in earlier works. Therefore, no additional information is needed to establish these advantages. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of common fixed point for three mappings in Gb-complete Gb-metric space. On the other hand, we prove that the theory is also established in G-metric space and several corollaries and examples are listed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new extragradient method with regularization for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in infinitedimensional Hilbert spaces, combining the regularization method and the technique of averaged operator, we prove the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ under mild conditions. [ABSTRACT FROM AUTHOR]

In this paper, we present new fixed point theorems for Kannan type Fp-contraction and Kannan type (α, η, GFp)-contraction on a closed ball contained in a complete partial metric space. Some comparative examples are constructed to illustrate the signifficance of these results. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper, we discuss the convergence theorems for the double acting iterative scheme to a common fixed point for a family of generalized φ-weak contraction mappings in CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, a concept of C*-algebra-valued modular metric space is introduced which is a generalization of a modular metric space of Chistyakov (Folia Math. 14 (2008), 3-25). Next, some common fixed point theorems are proved for generalized contraction type mappings on such spaces. Also, to support of our results an application is provided for existence and uniqueness of solution for a system of integral equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to obtain common fixed point theorem involving two pair of weakly compatible mappings in complete fuzzy metric spaces. Some related results and illustrative examples are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a new fixed point theorem in cones of Banach spaces. Then, we apply the fixed point theorem to study the existence and uniqueness of monotone positive solutions for an elastic beam equation u(4)(t) = f(t; u(t); u'(t)) with superlinear boundary conditions. An example is given to illustrate our main result. Compared with some earlier results (cf. [10]), the biggest differences are that we consider such equation with superlinear boundary conditions and remove some restrictive conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the septendecic functional equation and prove the Hyers-Ulam stability for the septendecic functional equation in matrix normed spaces by using the fixed point technique. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following cubic functional equation with involution f(2x + y) + f(2x + σ(y)) - 2f(x + y) - 2f(x + σ(y)) - 12f(x) = 0 in modular spaces by using a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the functional inequality N(f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 6f(y); t) ≥ N(f(2x + y) + f(2x - y) - 2f(x + y) - 2f(x - y) - 12f(x); kt) for some fixed nonzero real number k and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces by fixed point methods. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study the existence of solution of a system of differential equations using fixed point technique. In this regard, in the first part of this article, along with some properties of partial b-metric topology, we prove a common fixed point theorem for generalized Geraghty type contraction mappings in a complete partial b-metric spaces. Then in second part we apply this result to show the existence of the solution of a system of ordinary differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we study the mapping satisfying mixed g-monotone property in partially ordered complete Menger probabilistic G-metric spaces. By weakening the notion of Ψ, we prove some new coupled coincidence point theorems and coupled common fixed point theorems. Finally, we provide an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of fixed points for Kannan contraction, Chatterjea contraction and Reich contraction in setting of digital metric spaces. These digital con-tractions are the applications of metric fixed point theory contractions. [ABSTRACT FROM AUTHOR]

In this paper, by considering both F-contraction and fixed point results on ordered partial metric spaces, we introduce a pair of Círíc type ordered F-contractions on an ordered partial metric space. Then we give a common fixed point theorem for such contractions. We give an example showing that our main theorem is applicable, but both results of Durmaz et al. [11] and Wardowski [18] are not. We also discuss that this fixed point result can be applied to show the existence of solution of an integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new idea of α-C-class function and establish new fixed point results in a complete metric space. It can be stated that the results that have come into being give substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a solution of new type quintic functional equations and prove the Hyers-Ulam-Rassias stability for a quintic functional equation by the directed method and a subaddtive function approach and also, present a counterexample. Finally, we investigate the Hyers-Ulam-Rassias stability for a quintic functional equation with an involution by the fixed point method. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce several types of Meir-Keeler contractive mappings in the structure of Ms-metric spaces. Then we study some existence and uniqueness fixed point theorems for these types of MKC mappings in Ms-metric spaces via Gupta-Saxena type contraction and other fraction version type contractions. Also, we extend and improve very recent results in fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of C-class fuction, we prove the existence of common fixed point for generalized Zam rescu-type mappings and generalized weakly Zam rescu-type mappings. Our results generalize so many results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce dualistic contractive mappings and use such mappings to prove some fixed point theorems. The results extend various comparable results existing in the literature. Moreover, we give examples that show the superiority and effectiveness of our results among corresponding fixed point theorems in partial metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of coincidence points for two nonlinear operators by generalizing the notion of simulation function introduced by F. Khojasteh et al. [F. Khojasteh, S. Shukla and S. Radenović, Filomat 29 (6), 1189-1194 (2015)]. Our results improve, extend, complement and generalize several existing results in the literature. Also, some examples are provided to illustrate the usability of our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish common fixed point results on a sequence contained in a closed ball for family of multivalued mapping in complete fuzzy metric space. Simple and different technique has been used. Example has been constructed to demonstrate the novelty of our results. Our results unify, extend and generalize several results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we solve the additive (α, β)-functional equation f(x) + f(y) + 2f(z) = αf(β(x + y +2z)); (0.1) where α, β are fixed real or complex numbers with α ≠4 and αβ= 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (α,β)-functional equation (0.1) in Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, authors introduce the concepts of operator m- convex function and operator (α, m)-convex function, and establish some new in- tegral inequalities of Hermite-Hadamard type for operator m-convex and (α, m)- convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new iterative algorithms (one implicit and one explicit) for finding a common point of the set of zeros of an accretive operator and the set of fixed points of a nonexpansive mapping in a real uniformly convex Banach space having a uniformly Gâteaux differentiable norm. Then under suitable control conditions, we establish strong convergence of sequence generated by proposed algorithm to a common point of above two sets, which is a solution of a ceratin variational inequality. The main theorems develop and complement some well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove common fixed point theorems for two mappings under the condition of R-weakly commuting in complete S-metric spaces. A lot of fixed point theorems on ordinary metric spaces are special cases of our main result. [ABSTRACT FROM AUTHOR]

In this paper, utilizing the concepts of weakly biased mappings and occasionally weakly biased mappings for a pair of self-mappings in Menger PM-spaces, some new common fixed point theorems under contractive conditions are obtained. Some examples are also given to exemplify our main results. [ABSTRACT FROM AUTHOR]

Let φ be an analytic self-map of open unit disk 픽. A composition operator is defined as (Cφf)(z) = f(φ(z)), for z ∈ 픽and f analytic on 픽. Given an admissible weight w, the weighted Hilbert space Hw consists of all analytic functions f such that ... = |f(0)|² + ∫픽 |f'(z)\²w(z)dA(z) is finite. In this paper, we study composition operators acting between weighted Bergman space Aα² and the weighted Hilbert space Hw. Using generalized Nevalinna counting functions associated with w, we characterize the bounded-ness and compactness of these composition operators. [ABSTRACT FROM AUTHOR]

The study of iterated contraction was initiated by Rheinboldt in 1969. The concept of iterated contraction proves to be very useful in the study of certain iterative process and has wide applicability. In this paper a brief introduction of iterated contraction maps is given and some fixed point results are discussed. [ABSTRACT FROM AUTHOR]