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Abstract: We show that the main results in the recent paper [4] by Sadiq Basha (2012) are not real generalizations but particular cases of existing fixed point theorems in the literature. [Copyright &y& Elsevier]

In this paper, we present a new iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of common fixed points of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently. [ABSTRACT FROM AUTHOR]

This paper studies a class of global fractional-order projective dynamical systems involving set-valued perturbations in real separable Hilbert spaces. We prove that the set of solutions for this type of systems is nonempty and closed under some suitable conditions. Furthermore, we show that the set of solutions is continuous with respect to initial value in the sense of Hausdorff metric. Finally, an interesting numerical example is given to illustrate the validity of the main theorem presented in this paper. [ABSTRACT FROM AUTHOR]

Abstract In this paper, some new theorems for various cyclic contractions are established in G b -metric spaces to discuss the existence and uniqueness of the solutions for a class of the operator equations, which generalize many known results in corresponding literatures. On the other hand, we introduce the notion of the cyclic α - ψ φ-contractive mappings in G b -metric spaces and establish a new fixed point theorem, which is applied to consider the existence of the solutions of the integral equations and ordinary differential equations. Moreover, some examples are given to support our main results. [ABSTRACT FROM AUTHOR]

Abstract In the present paper we prove some new fixed point theorems for self-mappings defined on a complete metric space with a w -distance. These results extend some previous fixed point theorems in this field to more general contractive conditions in the setting of w -distances for selfmappings which satisfy certain weaker Meir–Keeler conditions. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for an infinite family of strictly pseudo-contractive mappings and the set of common fixed points for nonexpansive semi-groups in Hilbert space. Under suitable conditions some strong convergence theorem are proved. The results presented in the paper extend and improve some recent results. [Copyright &y& Elsevier]

Abstract: In this paper, we firstly make some corrections for typos errors on our paper “Nontrivial Solution of Third-order Nonlinear Eigenvalue Problems, Appl. Math. Comput. 176(2006), 714–721”. And then, we supplement some cases which have not been studied in the above paper. [Copyright &y& Elsevier]

In this paper, we obtain a maximum principle for the coupled system of second and fourth order elliptic equations using an abstract result in a recent paper by Correa and Souto [Nonlinear Anal. 26 (1996)] and an application of the maximum principle is given. [Copyright &y& Elsevier]

In this paper, we introduce the concept of monotone α -nonexpansive mappings in an ordered Banach space E with the partial order ≤, which contains monotone nonexpansive mappings as special case. With the help of the Mann iteration, we show some existence theorems of fixed points of monotone α -nonexpansive mappings in uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of the Mann iteration for finding an order fixed point of monotone α -nonexpansive mappings under the condition lim sup n → ∞ β n ( 1 − β n ) > 0 or lim inf n → ∞ β n ( 1 − β n ) > 0 . [ABSTRACT FROM AUTHOR]

In this paper we obtain some equivalences between cyclic contractions and non-cyclic contractions in the framework of b -metric spaces. Our results improve and complement several recent fixed point results for cyclic contractions in b -metric spaces established by George et al. (2015) and Nashine et al. (2014). Moreover, all the results are with much shorter proofs. In addition, an application to integral equations is given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper we study a second order retarded differential equation with variable delay. Applying the fixed point theory we obtain a necessary and sufficient condition ensuring that the zero solution of the equation is asymptotically stable. Our results improve and generalize the known ones in this direction. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalized contraction of Krasnoselskii-type using auxiliary functions, and obtained some sufficient conditions for existence and uniqueness of fixed point for such mappings on bimetric spaces. We also establish a result on coincidence point of two mappings, and derive several corollaries of our main theorems. As application, we establish an existence result for a two-point boundary value problem of second order differential equation. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the existence and the stability of solutions for Riemann–Liouville Volterra–Stieltjes quadratic integral equations of fractional order. Our results are obtained by using some fixed point theorems. Some examples are provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (2002) (see [6] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equations with functional delay x′(t)=-a(t)h(x(t-τ(t)))+d/dtQ(t,x(t-τ(t)))+G(t,x(t-τ(t))). The stability of the zero solution of this equation provided that h(0)=Q(t,0)=G(t,0,0)=0. The Caratheodory condition is used for the functions Q and G. [ABSTRACT FROM AUTHOR]

This paper focuses on the existence of a periodic solution of the delay neutral nonlinear dynamic systems x Δ(t)=A(t)x(t)+Q Δ(t, x(δ-(s, t)))+G(t, x(t) , x(δ-(s, t))) . In our analysis, we utilize a new periodicity concept in terms of shifts operators, which allows us to extend the concept of periodicity to time scales where the additivity requirement t±T∈T for all t∈T and for a fixed T>0, may not hold. More importantly, the new concept will easily handle time scales that are not periodic in the conventional way such as; qZ ‾; and #x222a;k=1∞ <[3±k ,2.3±]k∪{0}. Hence, we will develop the tool that enables us to investigate the existence of periodic solutions of q-difference systems. Since we are dealing with systems, in order to convert our equation to an integral systems, we resort to the transition matrix of the homogeneous Floquet system y Δ(t)=A(t)y(t) and then make use of Krasnoselskii's fixed point theorem to obtain a fixed point. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove strong convergence theorems for the Mann-type implicit process of a continuous hemicontractive mappings defined on a noncompact domain in real Hilbert spaces. [Copyright &y& Elsevier]

Abstract: In this paper, equilibrium and fixed point problems based on hybrid iterative processes are investigated. It is proved that the sequence generated in the purposed iterative process converges strongly to a common element in the fixed point set of an asymptotically strict pseudocontraction and in the solution set of an equilibrium problem in the framework of real Hilbert spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we present some results concerning the existence, the uniqueness and the attractivity of solutions for some functional integral equations of Riemann–Liouville fractional order, by using some fixed point theorems. [Copyright &y& Elsevier]

Abstract: The fixed point theorems presented in this paper generalize recent results of Dutta and Choudhury [3], Branciari [2], Banach [1], Rhoades [9], Khan et al. [6], Kada [5] and Rhoades and Abbas [10]. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence of integral solutions to a general nonlinear integral equationWith the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we establish a new and general existence theorem for the nonlinear functional integral equation. Moreover, an example, which can not be treated by the related theorems in [5,20,22], is given to illustrate the new existence theorem. [Copyright &y& Elsevier]

Abstract: In this paper, using the concept of attractive points of a nonlinear mapping, we obtain a strong convergence theorem of Halpern’s type [7] for nonexpansive mappings in a star-shaped subset of a Hilbert space. Using this result, we obtain a new fixed point theorem and a strong convergence theorem which generalizes Wittmann’s theorem [26]. [Copyright &y& Elsevier]

Abstract: In this paper, we obtained Suzuki type fixed point results for a generalized multi-valued mapping on a set equipped with two b-metrics. As a consequence, existence and uniqueness of solution of functional equation arising in dynamical programming is also derived. [Copyright &y& Elsevier]

Abstract: Main results of this paper are fixed point theorems for mappings with a generalized contractive iterate at a point in G-metric spaces which are generalizations of the well-known results in metric spaces. [Copyright &y& Elsevier]

Abstract: In this paper we present an improved acceleration method for solving nonlinear equations. The new acceleration technique was inspired by one derivation of Aitken’s process. Some numerical examples are given to illustrate the abilities of the new proposed acceleration technique. [Copyright &y& Elsevier]

Abstract: In this paper, we first introduce the concept of NR-map and then use this concept to establish the existence of common fixed points for Banach operator pairs in the context of uniformly convex geodesic metric spaces. New proofs of main results (Theorems 2.1 and 3.5) of Chen and Li [J. Chen, Z. Li, Banach operator pair and common fixed points for nonexpansive maps, Nonlinear Anal. 74 (2011) 3086–3090] are presented. Further, we prove De Marr’s theorem for the family of symmetric Banach operator pairs in metric spaces and -trees for single and multivalued mappings satisfying conditions that generalize the concept of nonexpansivity. [Copyright &y& Elsevier]

Abstract: In this paper, we study solvability of two functional equations arising in dynamic programming of multistage decision processes. By using Boyd and Wong fixed point theorem, some existence and uniqueness theorems of solutions and iterative approximation for solving these class of functional equations are established. The results presented here extend, improve and unify the corresponding results due to Bellman, Bhakta and Mitra, Bhakta and Choudhary, Liu and Kang, Liu et al., Jiang et al. and others. We also discuss some illustrative examples to highlight the realized improvements. [Copyright &y& Elsevier]

Abstract: In this paper, we study the almost periodic solution for a neutral multi-species Logarithmic population model. By employing Banach’s fixed point theorem and using differential inequality technique, we present some sufficient conditions ensuring the existence, uniqueness and globally exponential stability of almost periodic solution for the model. The results obtained extend and improve the earlier publications. Finally, two examples are provided to show the correctness of our analysis. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce some new iteration methods based on the hybrid method in mathematical programming, the Mann’s iterative method and the Halpern’s method for finding a fixed point of a nonexpansive mapping and a common fixed point of a nonexpansive semigroup Hilbert spaces. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to prove a strong convergence theorem for a pair of sequences of nonexpansive mappings in a Hilbert space, where one of them is a strongly nonexpansive sequence, and provide some applications of the theorem. [Copyright &y& Elsevier]

Abstract: In this paper, the parabolic quasi-variational inequalities are transformed into a noncoercive elliptic quasi-variational inequalities. A new iterative discrete algorithm is proposed to show the existence and uniqueness, and a simple proof to asymptotic behavior in uniform norm is also given using the theta time scheme combined with a finite element spatial approximation. The proposed approach stands on a discrete L ∞-stability property with respect to the right-hand side and obstacle defined as an impulse control problem. [Copyright &y& Elsevier]

Abstract: In this paper we prove some fixed points results on cone metric spaces for maps satisfying general contractive type conditions. Among other things, we extend some results of Nguyen from metric spaces to cone metric spaces. The example is included. [Copyright &y& Elsevier]

Abstract: We prove some fixed point and periodic point theorems for a map in generalized metric spaces. An example is provided to support our result. The results presented in this paper generalize several well known comparable results in the literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the stability and periodicity for a class of impulsive neural networks with delays. By means of the Fixed point theory, Lyapunov functional and analysis technique, some sufficient conditions of exponential stability and periodicity are obtained. We can see that impulses do contribution to the stability and periodicity. An example is given to demonstrate the effectiveness of the obtained results. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to introduce a general iterative method for finding a common element of the solution set of quasi-variational inclusion problems and of the common fixed point set of an infinite family of nonexpansive mappings in the framework Hilbert spaces. Strong convergence of the sequences generated by the purposed iterative scheme is obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce an iterative method for finding a common element in the solution set of generalized equilibrium problems, in the solution set of variational inequalities and in the common fixed point set of a family of nonexpansive mappings. Strong convergence theorems are established in the framework of Hilbert spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we considered the following four-point boundary value problemwhere By applying fixed-point theorems, we obtain a variety of existence results. In particular, our four-point boundary condition is a new kind Sturm–Liouville-like boundary condition, which has rarely been considered up to now. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we generalize and unify some results of Sehgal and Guseman, and Ćirić’s theorem for mappings with a generalized contractive iterate at a point to cone metric spaces, in which the cone does not need to be normal. As corollaries, we obtain recent results of Huang and Zhang, and Raja and Vaezpour. Furthermore, we introduce the definition of Fisher quasi-contractions on cone metric spaces and study their properties. Among other things, using new method of proof, we solve the open problem for the interval of contractive constant of (Ćirić) quasi-contraction in non-normal cone metric spaces, and as sn immediate corollary, we recover the recent result of Rezapour and Hamlbarani. [Copyright &y& Elsevier]

Abstract: This paper studies the soliton perturbation that are described by three nonlinear wave equations. The adiabatic dynamics of the soliton parameters and the soliton velocity is obtained, in the presence of perturbation terms. The fixed point is also determined in a couple of cases. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new W-mapping and present an iterative algorithm for an infinite family of strict pseudo-contractions. Strong convergence theorems are proved in Banach spaces. Our results improve and extend the corresponding result announced by Cai and Hu [G. Cai, C. Hu, Strong convergence theorems of modified Ishikawa iterative process with errors for an infinite family of strict pseudo-contractions, Nonlinear Anal. 71(12) (2009) 6044–6053]. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new composite iterative method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings. Our results improve and extend the corresponding ones announced by many others. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new iterative scheme for finding the common element of the set of common fixed points of infinitely many nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for -inverse-strongly monotone mapping in Hilbert spaces. We prove that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. This main result improve and extend Plubtieng and Punpaeng’s corresponding result [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings, Applied Mathematics and Computation 197 (2008), 548–558]. Using this theorem, we obtain three corollaries. [Copyright &y& Elsevier]

Abstract: In this paper, the concept of asymptotically hemi-pseudocontractive mapping in Banach space, which is a proper generalization of asymptotically pseudocontractive mapping with nonempty fixed point set as shown by an example, is introduced. Some sufficient and necessary conditions on the strong convergence of the modified Ishikawa and the modified Mann iteration sequences with mean errors for uniformly -Lipshitzian asymptotically hemi-pseudocontractive mappings are presented. [Copyright &y& Elsevier]

Abstract: In this paper, fixed point theorems of Rothe and Altman types about convex-power condensing operator are given and applied to the differential equation of one order with integral boundary conditions in abstract space. [Copyright &y& Elsevier]

Abstract: By using viscosity approximation methods for asymptotically nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for a new type of iterative sequences to converging to a fixed point which is also the unique solution of some variational inequalities are obtained. The results presented in the paper extend and improve some recent results in [C.E. Chidume, Jinlu Li, A. Udomene, Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 138 (2) (2005) 473–480; N. Shahzad, A. Udomene, Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal. 64 (2006) 558–567; T.C. Lim, H.K. Xu, Fixed point theories for asymptotically nonexpansive mappings, Nonlinear Anal. TMA, 22 (1994) 1345–1355; H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004) 279-291]. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Our results improve and extend the recent ones announced by Chen et al. [J.M. Chen, L.J. Zhang, T.G. Fan, Viscosity approximation methods for nonexpansive mappings and monotone mappings, doi:10.1016/j.jmaa.2006.12.088], Iiduka and Tahakshi [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350], Yao and Yao [Y.H. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput, doi:10.1016/j.amc.2006.08.062] and Many others. [Copyright &y& Elsevier]

Abstract: Recently, Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 2006, doi:10.1016/j.jmaa.2006.08.036] suggested and analyzed an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. In this paper, we introduce a new iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in a Hilbert space. Then, we prove a strong convergence theorem which is the improvements and extension of Takahashi and Takahashi’s (2006) corresponding result. Using this theorem, we obtain two corollaries which improve and extend their corresponding results. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. This main theorem extends a recent result of Yao and Yao [Y. Yao, J.-C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Applied Mathematics and Computation 186 (2) (2007) 1551–1558]. [Copyright &y& Elsevier]

Abstract: In this paper, we give an existence theorem for extremal solutions of a class of first order nonresonance impulsive dynamic equations on time scales with a periodicity condition. [Copyright &y& Elsevier]

Abstract: In this paper, we construct fractional iterates for piecewise differentiable maps. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce an extragradient-like approximation method which is based on so-called extragradient method and viscosity approximation method. We establish a strong convergence theorem for two iterative sequences generated by this method. [Copyright &y& Elsevier]