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Abstract: Huang and Zhang reviewed cone metric spaces in 2007 [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476]. We shall prove that there are no normal cones with normal constant and for each there are cones with normal constant . Also, by providing non-normal cones and omitting the assumption of normality in some results of [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476], we obtain generalizations of the results. [Copyright &y& Elsevier]

Abstract: W.A. Kirk [W.A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. 277 (2003) 645–650] defined the notion of an asymptotic contraction on a metric space and using ultrapower techniques he gave a nonconstructive proof of an asymptotic version of the Boyd–Wong fixed point theorem. Subsequently, I.D. Arand̄elović [I.D. Arand̄elović, On a fixed point theorem of Kirk, J. Math. Anal. Appl. 301 (2005) 384–385] established somewhat more general version of Kirk''s result and he gave an elementary proof of it. However, our purpose is to show that there is an error in this proof and, moreover, Arand̄elović''s theorem is false. We also explain how to correct this result. [Copyright &y& Elsevier]

This paper focuses on the effects of environmental improvement and worsening on the spread and invasion of populations with birth pulse. We propose an impulsive reaction-diffusion model with a shifting environment to describe the dynamics of species with distinct reproduction stage and dispersal stage. First, the impulsive reaction-diffusion model is reduced to a discrete-time recursive system defined by a discrete map. Next, with the aid of the appropriate test function and comparison principle, we obtain some sufficient conditions on the nonexistence and uniqueness of nontrivial fixed points of the discrete map. This, combined with the abstract theory of spatially non-translation dynamical systems, enables us to establish the existence of traveling wave solutions and the asymptotic propagation properties of the model. [ABSTRACT FROM AUTHOR]

• Formulation of TMD-PSEH system attached to an undamped primary structure. • Extension of the fixed point theory to the TMD-PSEH system. • Close-form expression of optimal tuning, damping, and resistance ratios. • Insight into the power flow analysis. • Performance of the system along with attendant numerical simulations. A tuned mass damper with a piezoelectric stack energy harvester (TMD-PSEH) is a passive vibration control device for the dual purpose of absorbing vibration and harvesting energy. This paper develops the fixed point theory for the optimal design of a TMD-PSEH attached to an undamped primary structure under harmonic external excitation. It has been proven that the existence of two fixed points of the amplitude-frequency curve doest not depend on the damping of the primary structure. Based on the requirements for suppressing the vibration of the primary structure and enlarging the harvested power, the analytical expressions for the optimal tuning, damping, and resistance ratios are determined. It is found that the minimum damping ratio occurs in the vicinity of the electrical resistance ratio α = 1 for various values of the electromechanical coupling coefficient. Power flow analysis is carried out resulting in closed-form expressions of instantaneous and average powers. Numerical examinations of the system with the obtained optimal parameters are performed demonstrating a very good compatibility between theory and computation. In addition, the effect of damping in the primary structure is also investigated. It is shown that not only the vibration of the primary structure effectively reduces, but also a large amount of the harvested energy can be captured in the main resonance region. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a modified Marcinkiewicz interpolation result, and using this result, we obtain a new regularity result for a fractional Laplacian problem on a bounded C 1 , 1 -domain Ω in R N , and we also obtain a new regularity result for then fractional problem on unbounded Ω = R N by using the Stampacchia truncation method. Next, by the Leray-Schauder fixed point theorem we obtain the existence of solutions for a class of fractional Laplacian problems with weak growth conditions on the nonlinearities. Finally, as an application, we prove the existence of positive solutions for a fractional Laplacian problem which has an exponential growth nonlinearity. [ABSTRACT FROM AUTHOR]

In a previous paper of ours we used the notion of porosity to show that most of the nonexpansive self-mappings of bounded, closed and convex subsets of a Banach space are contractive and possess a unique fixed point which is the uniform limit of all iterates. In this paper we extend this result to nonexpansive self-mappings of closed and convex sets in a Banach space which are not necessarily bounded. As a matter of fact, it turns out that our results are true for all complete hyperbolic metric spaces. [ABSTRACT FROM AUTHOR]

In 2008, T. Suzuki [33] defined one of most relevant extensions of the notion of nonexpansivity. This notion was extended in [15] defining the, so called, C λ -mappings. In the last years, some papers have appeared trying to extend the most important results about existence of fixed points for nonexpansive mappings to this wider class of mappings (see, for instance, [2,5,9,10,15] ). In this paper we continue this project proving that Banach spaces with extended unconditional bases satisfy the fixed point property for C λ -mappings if the unconditional constant of the basis is small enough. We also begin a new project on renorming with the fixed point property for C λ -mappings, proving that any separable Banach space can be renormed to satisfy the fixed point property for C λ -mappings in a stable sense, that is, the space with the new norm satisfies the fixed point property which, in addition, is inherited by those isomorphic spaces which are close to it in the sense of the Banach–Mazur distance. [ABSTRACT FROM AUTHOR]

Abstract In this paper we investigate fixed-point numbers and entropies of endomorphisms on abelian varieties. It was shown quite recently that the number of fixed-points of an iterated endomorphism on a simple complex torus is either periodic or grows exponentially. Criteria to decide whether a given endomorphism is of the one type or the other are still missing. Our first result provides such criteria for simple abelian varieties in terms of the possible types of endomorphism algebras. The number of fixed-points depends on the eigenvalues and we exactly show which analytic eigenvalues occur. This insight is also the starting point to ask for the entropy of an endomorphism. Our second result offers criteria for an endomorphism to be of zero or positive entropy. The entropy is computed as the logarithm of a real number and our third result characterizes the algebraic structure of this number. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with an operator equation on ordered Banach spaces, where A is an increasing α-concave operator, B is an increasing sub-homogeneous operator and C is a homogeneous operator. The existence and uniqueness of its positive solutions is obtained by using the properties of cones and a fixed point theorem for increasing general β-concave operators. As applications, we utilize the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for two classes nonlinear problems which include fourth-order two-point boundary value problems for elastic beam equations and elliptic value problems for Lane–Emden–Fowler equations. [Copyright &y& Elsevier]

In this paper, we define the class of ( α , β ) -nonexpansive mappings which is properly larger than the class of α -nonexpansive mappings and prove that every ( α , β ) -nonexpansive mapping T : C → C has an approximate fixed point sequence, where C is a nonempty bounded subset of a Banach space X , α > 0 and β ≥ 0 . This, in particular, gives an affirmative answer to the open question posed by Ariza-Ruiz and et al. concerning the existence of an approximate fixed point sequence for α -nonexpansive mappings, Ariza-Ruiz et al. (2016) [4] . [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and exponential stability of mild solutions for a class of impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup in Hilbert spaces. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Mönch fixed point theorem. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study the general solution of the following general radical quintic functional equation f ( a x 5 + b y 5 5 ) = r f ( x ) + s f ( y ) for f a mapping from the field of real numbers into a vector space, where a , b , r , s are fixed nonzero reals. Also, we prove the generalized hyperstability results for the general radical quintic functional equation by using the fixed point theorem (cf. Dung and Hang (2018) [15] , Theorem 2.1) in quasi- β -Banach spaces. Namely, we show, under some weak natural assumptions, functions satisfying the above equation approximately (in some sense) must be actually solutions to it. [ABSTRACT FROM AUTHOR]

The moduli R ( a , X ) and M ( X ) , introduced by Domínguez Benavides, play an important role in the fixed point theory for nonexpansive mappings. In the paper we show that if inf i ∈ I ⁡ M ( X i ) > 1 , then M ( ( ⨁ i ∈ I X i ) Z ) > 1 , where ( ⨁ i ∈ I X i ) Z is the direct sum of Banach spaces X i with respect to a Banach lattice Z , under some conditions for Z and I . Similar results are obtained for the modulus R ( a , X ) . [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce and analyze a new hybrid iterative algorithm for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of an infinite family of nonexpansive mappings. Furthermore, we prove some strong convergence theorems for the hybrid iterative algorithm under some mild conditions. We also discuss some special cases. Results obtained in this paper improve the previously known results in this area. [Copyright &y& Elsevier]

Abstract: In this paper the concept of a contraction for multi-valued mappings in a metric space is introduced and the existence theorems for fixed points of such contractions in a complete metric space are proved. Presented results generalize and improve the recent results of Y. Feng, S. Liu [Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006) 103–112], D. Klim, D. Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (2007) 132–139] and several others. The method used in the proofs of our results is new and is simpler than methods used in the corresponding papers. Two examples are given to show that our results are genuine generalization of the results of Feng and Liu and Klim and Wardowski. [Copyright &y& Elsevier]

Abstract: Let X be a Banach space whose dual space is uniformly convex. We demonstrate that, for any demicontinuous, weakly Nagumo, k-pseudo-contractive mapping with closed domain, weakly generates a semigroup on . In this paper, we project the consequences of this result on fixed point theory. In particular, we show that if (id est, if T is strongly pseudo-contractive), then T has a unique fixed point. This implies that, if T is pseudo-contractive () and is closed, bounded, and convex, then T has at least one fixed point. Consequently, any demicontinuous pseudo-contractive mapping (for an appropriate C) has a fixed point, which has been an important open question in fixed point theory for quite some time. In a subsequent paper, we explore the consequences of the semigroup result on the existence of solutions to certain partial differential equations. The semigroup result directly implies the existence of unique global solutions to time evolution equations of the form where A is a combination of derivatives. The fixed point results from this paper imply the existence of solutions to partial differential equations of the form . [Copyright &y& Elsevier]

Abstract: The concept of weak contraction from the case of single-valued mappings is extended to multi-valued mappings and then corresponding convergence theorems for the Picard iteration associated to a multi-valued weak contraction are obtained. The main results in this paper extend, improve and unify a multitude of classical results in the fixed point theory of single and multi-valued contractive mappings and also improve recent results from the paper [P.Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl. 192 (1995), 655–666]. [Copyright &y& Elsevier]

Abstract: As an important iteration, the Mann and Ishikawa iteration has extensive application in fixed point theory. In 1991, David Borwein and Jonathan Borwein proved the convergence of the Mann iteration on a closed bounded interval in their paper. In this paper, we will extend their result to an arbitrary interval and to the Ishikawa iteration, indicating the necessary and sufficient condition for the convergence of Ishikawa iteration of continuous functions on an arbitrary interval. [Copyright &y& Elsevier]

In this paper, by using a new fixed point alternative, we establish a new generalization of the Hyers-Ulam-Rassias stability concerning a Cauchy-Jensen functional equation in normed spaces which are not necessarily Banach spaces. Moreover, our paper consists of several non-trivial examples which signify the motivation of such investigations. [ABSTRACT FROM AUTHOR]

In this paper, we study the hyperstability for the general linear equation in the setting of quasi-Banach spaces. We first extend the fixed point result of Brzdek et al. [5, Theorem 1] in metric spaces to b -metric spaces, in particular to quasi-Banach spaces. Then we use this result to generalize the main results on the hyperstability for the general linear equation in Banach spaces to quasi-Banach spaces. We also show that we can not omit the assumption of completeness in [5, Theorem 1] . As a consequence, we conclude that we need more explanations to replace a normed space by its completion in the proofs of some results in the literature. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study shape preserving properties of univariate Lototsky–Bernstein operators L n ( f ) based on Lototsky–Bernstein basis functions. The Lototsky–Bernstein basis functions b n , k ( x ) ( 0 ≤ k ≤ n ) of order n are constructed by replacing x in the i th factor of the generating function for the classical Bernstein basis functions of degree n by a continuous nondecreasing function p i ( x ) , where p i ( 0 ) = 0 and p i ( 1 ) = 1 for 1 ≤ i ≤ n . These operators L n ( f ) are positive linear operators that preserve constant functions, and a non-constant function γ n p ( x ) . If all the p i ( x ) are strictly increasing and strictly convex, then γ n p ( x ) is strictly increasing and strictly convex as well. Iterates L n M ( f ) of L n ( f ) are also considered. It is shown that L n M ( f ) converges to f ( 0 ) + ( f ( 1 ) − f ( 0 ) ) γ n p ( x ) as M → ∞ . Like classical Bernstein operators, these Lototsky–Bernstein operators enjoy many traditional shape preserving properties. For every ( 1 , γ n p ( x ) ) -convex function f ∈ C [ 0 , 1 ] , we have L n ( f ; x ) ≥ f ( x ) ; and by invoking the total positivity of the system { b n , k ( x ) } 0 ≤ k ≤ n , we show that if f is ( 1 , γ n p ( x ) ) -convex, then L n ( f ; x ) is also ( 1 , γ n p ( x ) ) -convex. Finally we show that if all the p i ( x ) are monomial functions, then for every ( 1 , γ n + 1 p ( x ) ) -convex function f , L n ( f ; x ) ≥ L n + 1 ( f ; x ) if and only if p 1 ( x ) = ⋯ = p n ( x ) = x . [ABSTRACT FROM AUTHOR]

In this article, by introducing a new set and a new concept of φ − ( h , e ) -concave operators, and by using the cone theory and monotone iterative method, we present some new existence and uniqueness theorems of fixed points for increasing φ − ( h , e ) -concave operators without requiring the existence of upper and lower solutions. As an application, we establish the existence and uniqueness of a nontrivial solution for a new form of fractional differential equation with integral boundary conditions. The main results of this paper improve and extend some known results, and present a new method to study nonlinear equation problems. [ABSTRACT FROM AUTHOR]

In this paper we prove the admissibility of modular function spaces E ρ considered and defined by Kozłowski in [17] . As an application we get that any compact and continuous mapping T : E ρ → E ρ has a fixed point. Moreover, we prove that the same holds true for any retract of E ρ . [ABSTRACT FROM AUTHOR]

A generalized Catalan matrix (a n , k) n , k ≥ 0 is generated by two seed sequences s = (s 0 , s 1 , ...) and t = (t 1 , t 2 , ...) together with a recurrence relation. By taking s ℓ = 2 ℓ + 1 and t ℓ = ℓ 2 we can interpret a n , k as the number of partial permutations, which are n × n 0 , 1 -matrices of k zero rows with at most one 1 in each row or column. In this paper we prove that most of fundamental statistics and some set-valued statistics on permutations can also be defined on partial permutations and be encoded in the seed sequences. Results on two interesting permutation families, namely the connected permutations and cycle-up-down permutations, are also given. [ABSTRACT FROM AUTHOR]

In this paper we prove that compactness can be characterized by means of the existence of a fixed point for some classes of mappings defined on convex closed subsets of the space ℓ 1 . Nominally, our result involves nonexpansive mappings, uniformly Lipschitzian mappings and cascading nonexpansive mappings. We also extend the results to some more general classes of Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, using the theory of fixed point index, we prove some results on the multiplicity of positive solutions for a class of nonlocal elliptic problem. [ABSTRACT FROM AUTHOR]

In this paper we investigate fixed-point numbers of endomorphisms on complex tori. Specifically, motivated by the asymptotic perspective that has turned out in recent years to be so fruitful in Algebraic Geometry, we study how the number of fixed points behaves when the endomorphism is iterated. Our first result shows that the fixed-points function of an endomorphism on a two-dimensional complex torus can have only three different kinds of behaviours, and we characterize these behaviours in terms of the analytic eigenvalues. Our second result focuses on simple abelian surfaces and provides criteria for the fixed-points behaviour in terms of the possible types of endomorphism algebras. [ABSTRACT FROM AUTHOR]

In this paper, we establish the demiclosedness principle for the class of mean nonexpansive mappings, introduced in 2007 by Goebel and Japón Pineda, defined on closed, convex subsets of Banach spaces satisfying Opial's condition. We also establish the demiclosedness principle for a subclass of the mean nonexpansive maps whose domains are closed, bounded, convex sets in uniformly convex spaces. These results extend known demiclosedness results for nonexpansive maps and lead to some fixed point results for mean nonexpansive maps which partially answer an open question posed by Goebel and Japón Pineda. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a coincidence point theorem for sequentially weakly continuous maps. Moreover, as a consequence, a critical point theorem for functionals possibly containing a nonsmooth part is obtained. Finally, as an application, existence results for nonlinear differential problems depending also on the derivative of the solution are established. [ABSTRACT FROM AUTHOR]

A well-known result of W. Ray asserts that if C is an unbounded convex subset of a Hilbert space, then there is a nonexpansive mapping T : C → C that has no fixed point. In this paper we establish some common fixed point properties for a semitopological semigroup S of nonexpansive mappings acting on a closed convex subset C of a Hilbert space, assuming that there is a point c ∈ C with a bounded orbit and assuming that certain subspace of C b ( S ) has a left invariant mean. Left invariant mean (or amenability) is an important notion in harmonic analysis of semigroups and groups introduced by von Neumann in 1929 [28] and formalized by Day in 1957 [5] . In our investigation we use the notion of common attractive points introduced recently by S. Atsushiba and W. Takahashi. [ABSTRACT FROM AUTHOR]

Let C be a closed, bounded and convex subset of a uniformly convex and uniformly smooth Banach space. Let { T t } t ≥ 0 be a strongly-continuous nonexpansive semigroup on C . Consider the iterative process defined by the sequence of equations x k + 1 = c k T t k + 1 ( x k + 1 ) + ( 1 − c k ) x k . We prove that, under certain conditions, the sequence { x k } converges weakly to a common fixed point of the semigroup { T t } t ≥ 0 . There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property. However, many important spaces like L p for 1 ≤ p ≠ 2 do not possess the Opial property. In this paper, we do not assume the Opial property. We do assume instead that X is uniformly convex and uniformly smooth. L p for p > 1 are prime examples of such spaces. [ABSTRACT FROM AUTHOR]

In this paper, criteria for uniform nonsquareness and locally uniform nonsquareness of Orlicz–Bochner function spaces equipped with the Orlicz norm are given. Although, criteria for uniform nonsquareness and locally uniform nonsquareness in Orlicz function spaces were known, we can easily deduce them from our main results. Moreover, we give a sufficient condition for an Orlicz–Bochner function space to have the fixed point property. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we extend Mizoguchi–Takahashi's fixed point theorem for multi-valued mappings on a metric space endowed with a graph. As an application, we establish a fixed point theorem on an ε-chainable metric space for mappings satisfying Mizoguchi–Takahashi contractive condition uniformly locally. Also, we establish a result on the convergence of successive approximations for certain operators (not necessarily linear) on a Banach space as another application. Consequently, this result yields the Kelisky–Rivlin theorem on iterates of the Bernstein operators on the space and also enables us study the asymptotic behaviour of iterates of some nonlinear Bernstein type operators on . [Copyright &y& Elsevier]

Abstract: Let be a metric space with a K-valued non-Archimedean metric p. In this paper, we prove the existence and approximation of a fixed point for operators satisfying the contractive condition in the form , where is an increasing operator. Then, we study the generalized Ulam–Hyers stability of fixed point equations. We next obtain an extension of the Krasnoselskii fixed point theorem for the sum of two operators. Finally, an application to functional equations is given. [Copyright &y& Elsevier]

Abstract: In this paper, we provide several extensions of the Abian–Brown Fixed Point Theorem from single-valued mappings to set-valued mappings on chain-complete posets. Then we examine some non-monetized, non-cooperative games where both the collections of the strategies and the ranges of the utilities for the players are posets. By applying the extensions of the Abian–Brown Fixed Point Theorem and by applying the order-preserving property of mappings, we prove some existence theorems of extended and generalized Nash equilibria for non-monetized, non-cooperative games on chain-complete posets. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the notion of generalized hybrid sequences, extending the notion of nonexpansive sequences introduced and studied in our previous work Djafari Rouhani (1981, 1990, 1990, 1997, 2002, 2004, 2002) [2–8], and prove ergodic and convergence theorems for such sequences in a Hilbert space . Subsequently, we apply our results to prove new fixed point theorems for generalized hybrid mappings, first introduced in Kocourek et al. (2010) [14], Takahashi and Takeuchi (2011) [20], defined on arbitrary nonempty subsets of . [Copyright &y& Elsevier]

Abstract: In this paper, we mainly consider the properties of differences of meromorphic solutions for the difference equation concerning a Gamma function, where and are nonzero polynomials. By these properties, we deduce that a Gamma function satisfies that for every , and have same zeros, at most except exceptional zeros, where denotes the order of growth of a meromorphic function , and and denote the exponents of convergence of fixed points and zeros of respectively. [Copyright &y& Elsevier]

Abstract: In this paper, we study the problem of solving multivalued mixed variational inequalities. By using some sequential approximation techniques of fixed point theory, we solve the multivalued mixed variational inequalities involving locally Lipschitzian or locally cocoercive multivalued mappings. We establish that the convexity of the multivalued mapping values is not needed and construct by using the Banach contraction principle converging sequences to the solutions. Also, we show how to choose regularization parameters to compute these solutions. [Copyright &y& Elsevier]

Abstract: Let be a complete 2-uniformly convex metric space. Let be a nonempty, bounded, closed, and convex subset of , and let be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined by converges in a weaker sense to a fixed point of . [Copyright &y& Elsevier]

Abstract: The problem of finding the zeros of the sum of two maximally monotone operators is of fundamental importance in optimization and variational analysis. In this paper, we systematically study Attouch–Théra duality for this problem. We provide new results related to Passty’s parallel sum, to Eckstein and Svaiter’s extended solution set, and to Combettes’ fixed point description of the set of primal solutions. Furthermore, paramonotonicity is revealed to be a key property because it allows for the recovery of all primal solutions given just one arbitrary dual solution. As an application, we generalize the best approximation results by Bauschke, Combettes and Luke [H.H. Bauschke, P.L. Combettes, D.R. Luke, A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space, Journal of Approximation Theory 141 (2006) 63–69] from normal cone operators to paramonotone operators. Our results are illustrated through numerous examples. [Copyright &y& Elsevier]

Abstract: A remarkable fundamental theorem established by Mehta plays an important role in proving existence of fixed points, maximal elements, and equilibria in abstract economies. In this paper, we extend Himmelbergʼs measure of precompactness to the general setting of -spaces and obtain a generalization of Mehtaʼs theorem. As an application, we develop some new fixed point theorems involving a kind of condensing mappings. [Copyright &y& Elsevier]

Abstract: In this paper, we present a study of the dynamics of disjunctive networks under all block-sequential update schedules. We also present an extension of this study to more general fair periodic update schedules, that is, periodic update schedules that do not update some elements much more often than some others. Our main aim is to classify disjunctive networks according to the robustness of their dynamics with respect to changes of their update schedules. To study this robustness, we focus on one property, that of being able to cycle dynamically. [Copyright &y& Elsevier]

Abstract: In this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing Henstock–Kurzweil integrable functions. [Copyright &y& Elsevier]

Abstract: Let X be a uniformly convex Banach space with the Opial property. Let be an asymptotic pointwise nonexpansive mapping, where C is bounded, closed and convex subset of X. In this paper, we prove that the generalized Mann and Ishikawa processes converge weakly to a fixed point of T. In addition, we prove that for compact asymptotic pointwise nonexpansive mappings acting in uniformly convex Banach spaces, both processes converge strongly to a fixed point. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce two new classes of generalized nonexpansive mapping and we study both the existence of fixed points and their asymptotic behavior. [Copyright &y& Elsevier]

Abstract: The biologist René Thomas conjectured, twenty years ago, that the presence of a negative feedback circuit in the interaction graph of a dynamical system is a necessary condition for this system to produce sustained oscillations. In this paper, we state and prove this conjecture for asynchronous automata networks, a class of discrete dynamical systems extensively used to model the behaviors of gene networks. As a corollary, we obtain the following fixed point theorem: given a product X of n finite intervals of integers, and a map F from X to itself, if the interaction graph associated with F has no negative circuit, then F has at least one fixed point. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence for impulsive semilinear differential equations with nonlocal conditions. Using the techniques of approximate solutions and fixed point, existence results are obtained, for mild solutions, when the impulsive functions are only continuous and the nonlocal item is Lipschitz in the space of piecewise continuous functions, is not Lipschitz and not compact, is continuous in the space of Bochner integrable functions, respectively. [Copyright &y& Elsevier]

Abstract: This paper considers existence of multiple positive fixed points for some nonlinear operators, a particular case of the operators is sum of an e-concave operator and an e-convex operator. Then we apply the results to nonlinear integral equations. [Copyright &y& Elsevier]

Abstract: This paper investigates the existence of solutions for a class of weighted -Laplacian ordinary system boundary value problems, the sufficient conditions for the existence of solutions have been given via Leray–Schauder''s degree, and the existence of multiple solutions has been discussed via critical point theory. As an application, we discussed the existence of the radial solutions for the -Laplacian partial differential system boundary value problems. [Copyright &y& Elsevier]