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In this paper, we define fuzzy weak P-property. Then we prove a fuzzy best proximity point theorems for δ-contractions with condition fuzzy weak P-property. Later, we give definition of fuzzy isometric distance between two functions in non-Archimedean fuzzy metric spaces. Also, we introduce δ-proximal contraction type-1 and type-2 contraction respectively via functions preserving fuzzy isometric distance and providing fuzzy isometry. Then, we obtain some fuzzy best proximity results for -proximal contractions types in non-Archimedean fuzzy metric spaces. Finally, we present some examples to illustrate the validity of the definitions and results obtained in the paper. [ABSTRACT FROM AUTHOR]

Recently, the idea of φ-fixed point and the elementary results on φ-fixed points were first investigated by Jleli et al. [Jleli M, Samet B, Vetro C (2014) Fixed point theory in partial metric spaces via φ-fixed point's con- cept in metric spaces. Journal of Inequalities and Applications, 2014(1):1- 9.]. Based on this work, Karapinar et al. [Karapinar E, O'Regan D, Samet B (2015) On the existence of fixed points that belong to the zero set of a certain function. Fixed Point Theory and Applications, 2015(1):1-14.] established the new φ-fixed point results, which can be reduced to the famous fixed point result of Boyd and Wong in 1969. However, the main result of Karapinar et al. does not cover the φ-fixed point results of Jleli et al. This paper aims to fulfill this gap by proving φ-fixed point results covering several φ-fixed point results and fixed point results [ABSTRACT FROM AUTHOR]

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 consider and analyze a general iterative method to approximate a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping, which is the unique solution for the variational inequality in real Hilbert spaces. Furthermore, under reasonable conditions, the sequence generated by the proposed iterative scheme converges strongly to a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping, which is a solution of a certain optimization problem related to a strongly positive linear operator. The results presented in this paper improve and extend the corresponding results reported by some authors recently. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the generalized viscosity implicit rules of one asymptotically nonexpansive mapping in Hilbert spaces. We obtain some strong convergence theorems under certain assumptions imposed on the parameters. We also apply our main results to solve mixed equilibrium problem in Hilbert spaces. A numerical example is also given to support our main results. The results obtained in this paper improve and extend many recent ones in this field. [ABSTRACT FROM AUTHOR]

Recently, the idea of φ-fixed point and the elementary results on φ-fixed points were first investigated by Jleli et al. [Jleli M, Samet B, Vetro C (2014) Fixed point theory in partial metric spaces via φ-fixed point's concept in metric spaces. Journal of Inequalities and Applications, 2014(1):1-9.]. Based on this work, Karapinar et al. [Karapinar E, O'Regan D, Samet B (2015) On the existence of fixed points that belong to the zero set of a certain function. Fixed Point Theory and Applications, 2015(1):1-14.] established the new φ-fixed point results, which can be reduced to the famous fixed point result of Boyd and Wong in 1969. However, the main result of Karapinar et al. does not cover the φ-fixed point results of Jleli et al. This paper aims to fulfill this gap by proving φ-fixed point results covering several φ-fixed point results and fixed point results. [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]

In this paper, an uncountable infinite family of nonlinear mappings are investigated. Strong convergence theorems of common solutions are established in a strictly convex and uniformly smooth Banach space which also has the Kadec-Klee property. The results obtained in this paper unify and improve many corresponding results announced recently. [ABSTRACT FROM AUTHOR]

In this paper, based on the work by Moudafi and inspired by Takahashi and Xu, we try to investigate the split common fixed point problems for the class of demicontractive mappings in the setting of two Banach spaces, and obtain the strong and weak convergence theorems. The results presented in the paper improve and extend some recent well-known corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, some strong and Δ-convergence results for Suzuki generalized nonexpansive mappings in the setting of complete CAT(0) spaces are proved. We are using newly introduced K* iteration process for approximation of fixed point. We also give an example to show the efficiency of the K* iteration process. Our results are exten- sion, improvement and generalization of many well known results in the literature of fixed point theory in CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following new type cubic-quartic (CQ) functional equation where λ ≥ 2 is a fixed integer. We investigate the general solution of the functional equation, and then, using the fixed point method, we prove some stability results for this functional equation in matrix fuzzy normed spaces. [ABSTRACT FROM AUTHOR]

The purposes of this paper are to introduce and study some existence and convergence theorems for fixed points of a strict pseudo-contraction in the framework of complete CAT(0) spaces. By using available properties in the spaces together with some appropriate conditions of the mapping and under certain assumptions, we can create some suitable sets to be used to construct an iterative projection algorithm to guarantee the existence fixed points for a strict pseudo-contraction. The method allows us to obtain a strong convergence iteration for finding some fixed points of a strict pseudo-contraction in the framework of complete CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point theorems for non-self mappings, which solve the problem 1 in [1], satisfying special contractive conditions in complete metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iterative process for approximation of a common fixed point for a finite family of multi-valued Bregman relatively nonexpansive mappings with a solution of the split feasibility problems in p-uniformly convex and uniformly smooth Banach spaces. We prove the strong convergence theorems of the proposed iterative process in p-uniformly convex and uniformly smooth Banach spaces and present the numerical results to verify the efficiency and implementation of our results. [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 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 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 significance of these results. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. [ABSTRACT FROM AUTHOR]

By applying Krasnoselskii's and O'Regan's fixed point theorems, in this paper, we study the existence of solutions for a coupled system consisting from Langevin fractional differential equations of Riemann-Liouville type subject to the generalized nonlocal integral boundary conditions. Examples illustrating our results are also presented. [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]

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]

This paper aims to study the existence of the solutions for an Impulsive Sequential Fractional Differential Equations of order 1 < q ≤ 2 involving separate boundary conditions. Our analysis relies on some fixed point theorems. In addition, an example is provided to illustrate the results of this study. [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]

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 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 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]

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, 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 prove the existence of fixed points for Kannan contraction, Chat- terjea 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, we introduce a viscosity rule for common fixed points of two non-expansive mappings in Hilbert spaces. The strong convergence of this technique is proved under certain assumptions imposed on the sequence of parameters. [ABSTRACT FROM AUTHOR]

In this paper, some notions are introduced in modular metric spaces. Next some common fixed points are established in ω-orbitally complete modular metric spaces by employing C-class functions that extend and generalize the results of [10, 18]. Finally, for usibility of our results an application is provided to show the existence of solutions for certain system of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we, motivated by Mihet [2], give the concept of two nonlinear contractions ((φ, ε-λ)-contraction and (f, bn)-contraction) in KM-fuzzy metric spaces, and obtained some fixed point theorems. We answer the open question posed by Mihet in [2, open question 2]. Finally, an example can be used to be exemplify our results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some coupled fixed point results for two mappings satisfying some contractive conditions in cone b-metric spaces over Banach algebras with a solid cone by virtue of the properties of spectral radius. Also we give an example as an applications of one of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we present some properties of dual partial metric (abbreviation, pmetric) topology and investigate a fixed point result for self mappings in dual pmetric space. This result gener-alizes Banach contraction principle in a different way than in the known results from the literature. The article includes an example which shows the validity of our result. [ABSTRACT FROM AUTHOR]

In this paper, we develop some fixed point theorems by using auxiliary functions for maps satisfying a rational type contractive condition in partially ordered S-metric spaces. Conditions for uniqueness of fixed point are also discussed. Our results generalize some existing results in the literature of S-metric spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Alghamdi et al. [The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), Article ID 96, 9 pages] associated with Φ-hemicontractive mappings in a nonempty convex subset of an arbitrary Banach space. [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 give a multivalued version of Picard-Mann hybrid iterative process of Khan [4] in Kohlenbach hyperbolic space. This process converges faster than all of Picard, Mann and Ishikawa iterative processes. By using an idea of Shahzad and Zegeye [8] which removes a restriction on the mapping and the method of direct construction of Cauchy sequence as illustrated by Song and Cho [9], we obtain strong and Δ-convergence theorems of this process for a multivalued mapping. Our results improve corresponding results of Shazad and Zegeye [8], Song and Cho [9] and many other in the contemporary literature in terms of faster iteration, more general space and weaker condition on mapping T. [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]

By applying Krasnoselskii's and O'Regan's fixed point theorems, in this paper, we study the existence of solutions for a coupled system consisting from Langevin fractional differential equations of Riemann-Liouville type subject to the generalized nonlocal integral boundary conditions. Examples illustrating our results are also presented. [ABSTRACT FROM AUTHOR]

this paper, we generalize the notion of Meir-Keeler contraction condition in Mb- metric spaces. We prove some fixed point theorems for this class of contractions which enables us to extend and generalize the recent results of Gholmian and Khanehgir [2]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and solve the following quadratic (ρ1, ρ2)-functional inequality ... in fuzzy normed spaces, where ρ1 and ρ2 are fixed nonzero real numbers with ... < 1, and f (0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ1, ρ2)- functional inequality (0.1) in fuzzy Banach spaces. [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, we introduce a new concept of p-mean piecewise pseudo almost periodic for a stochastic process and establish a new composition theorem about pseudo almost periodic functions under non-Lipschitz conditions. Using this composition theorem, the analytic semigroup theory and fixed point strategy with stochastic analysis theory, we also study the existence and the global attractiveness for p-mean piecewise pseudo almost periodic mild solutions for impulsive partial neutral stochastic neutral functional differential equations. Moreover, an example is given to illustrate the general theorems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study a class of new two-step viscosity iteration methods for approximating fixed points of set-valued nonexpansive mappings in CAT(0) spaces. Here, the fixed point is unique solution of a variational inequality with a contraction mapping. Further, we prove strong convergence theorem of the two-step viscosity iterations with some general conditions in a complete CAT(0) space. The presented results improve and unify the corresponding results in the literature. [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 are concerned with the existence of positive solutions of the fully third-order boundary value problem ..., where f: [0, 1] x ℝ+ x ℝ+ x ℝ → ℝ is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that f (t, x, y, z) may be superlinear or sublinear growth on x, y and z as |(x, y, z)| → 0 and |(x, y, z)| → ∞. [ABSTRACT FROM AUTHOR]