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This paper is concerned with the problem of elliptic equations in annular domains involving derivative terms. Using nonlinear analysis methods, some results regarding existence of solutions are established. More precisely, at least one radial solution is obtained basing on Schauder's fixed point theorem and contraction mapping theorem, respectively. Some iterative technique is also applied, which allows us to overcome difficulties that the nonlinearity is related to derivative terms. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, existence results are derived for the unique, smallest, greatest, minimal, and/or maximal solutions of finite systems of nonlinear distributional Cauchy problems. The dependence of solutions on the data is also studied. Applications to systems of distributional differential equations with impulses and to higher-order distributional Cauchy problems are presented. The main tools are fixed point results in function spaces and a primitive integral of distributions defined in the paper, including recently introduced regulated and continuous primitive integrals on compact intervals. [Copyright &y& Elsevier]

Abstract: The purpose of this article is to propose a new hybrid algorithm with variable coefficients and prove convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense on unbounded domains. The results of the paper improve and extend the recent results of Qin et al. [X.L. Qin, S.Y. Cho, J.K. Kim, Convergence theorems on asymptotically pseudocontractive mappings in the intermediate sense, Fixed Point Theory Appl. 2010, doi:10.1155/2010/186874, Article ID 186874, 14 pages] and several others. The algorithm with variable coefficients introduced in this paper is of independent interest. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present some new fixed point theorems for mixed monotone operators with perturbation by using the properties of cones and a fixed point theorem for mixed monotone operators. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce hybrid pseudo-viscosity approximation schemes with strongly positive bounded linear operators for finding a common element of the set of solutions to a system of equilibrium problems, the set of fixed points of an infinite family and left amenable semigroup of non-expansive mappings in the frame work of Hilbert spaces. Our goal is to prove a result of strong convergence for hybrid pseudo-viscosity approximation schemes to approach a solution of systems of equilibrium problems which is also a common fixed point of an infinite family and left amenable semigroup of non-expansive mappings. The results presented in this paper can be treated as an extension and improvement of the corresponding results announced by Ceng et al. [L.C. Ceng, Q.H. Ansari, and J.C. Yao, Hybrid pseudo-viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many non-expansive mappings, Nonlinear Analysis 4 (2010) 743–754] and many others. [Copyright &y& Elsevier]

Abstract: The present paper is divided into two parts. In the first part, we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real Hilbert space. We establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping. Such a fixed point is also a solution of a variational inequality defined on the set of fixed points. In the second part, we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem. Such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping. The results of this paper extend and improve several results presented in the literature in the recent past. [Copyright &y& Elsevier]

Abstract: In this paper, we first introduce a general iterative scheme by Halpern approximation method for finding a common element of the set of solutions of an equilibrium problem, the set of solutions of the variational inequality for an infinite family of -inverse-strongly monotone mappings and the set of common fixed points for a family of infinitely nonexpansive mappings in a Hilbert space. Then, we extend the Halpern iterative scheme to a general viscosity approximation scheme by a simple and different method. As applications, we utilize our results to investigate some convergence problems for strictly pseudocontractive mappings and maximal monotone operators. The results obtained in this paper extend and improve the recent ones announced by many others. [Copyright &y& Elsevier]

Abstract: In this paper we introduce the concept of set-valued contractions in cone metric spaces and establish new endpoint and fixed point theorems for such contractions. The paper includes examples. [Copyright &y& Elsevier]

Abstract: This paper deals with the existence of multiple solutions for weighted -Laplacian equation Dirichlet problems. Several sub-super-solution type results have been given via Leray–Schauder’s degree method. In particular, we give a counterexample which means that in paper [J. Henderson, H.B. Thompson, Existence of multiple solutions for second order boundary value problems, J. Differential Equations 166 (2000) 443–454] is not an open subset of . [Copyright &y& Elsevier]

Abstract: In this paper, we study a class of nonlinear value boundary problems for second order differential inclusions with nonlinear perturbations, which satisfy the generalized Hartman condition weaker than that considered in some papers. Using techniques from multivalued analysis, theory of monotone operators and fixed points, we prove the existence of solutions in both “convex” and “nonconvex” cases. Our framework can be incorporated with Dirichlet, Neumann, and mixed boundary problems. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for -inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings. The results presented in the paper extend and improve some recent results of Yao and Yao [Y.Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2) (2007) 1551–1558], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings, Appl. Math. Comput. (2007) doi:10.1016/j.amc.2007.07.075], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for Equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2006) 506–515], Su, Shang and Qin [Y.F. Su, M.J. Shang, X.L. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. (2007) doi:10.1016/j.na.2007.08.045] and Chang, Cho and Kim [S.S. Chang, Y.J. Cho, J.K. Kim, Approximation methods of solutions for equilibrium problem in Hilbert spaces, Dynam. Systems Appl. (in print)]. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence of positive almost automorphic solutions to some nonlinear delay integral equations. We first establish a new fixed point theorem for mixed monotone operator in a cone, and then, with its help, we obtain existence theorems of positive almost automorphic solutions. Some examples are given to illustrate our results. As one will see, even in the case of almost periodicity, our theorems extend some earlier results, and moreover, the approach dealing with the integral equation arising in an epidemic problem in this paper is also new. [Copyright &y& Elsevier]

Abstract: In this paper, we suggest and analyze some new extragradient iterative methods for finding the common element of the fixed points of a nonexpansive mapping and the solution set of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We also consider the strong convergence of the proposed method under some mild conditions. Several special cases are also discussed. Results proved in this paper may be viewed as improvement and refinement of the previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of finitely many nonexpansive mappings. We prove that the approximate solution converges strongly to a solution of a class of variational inequalities under some mild conditions, which is the optimality condition for some minimization problem. We also give some comments on the results of Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 336 (2007) 455–469]. Results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this area. [Copyright &y& Elsevier]

Abstract: In this paper, using a generalization of the Fan–Browder fixed point theorem, we obtain a new fixed point theorem for multivalued maps in generalized convex spaces from which we derive several coincidence theorems and existence theorems for maximal elements. Applications of these results to generalized equilibrium problems and minimax theory will be given in the last sections of the paper. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extended and improved the results of H. Iiduka and W. Takahashi [Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350] and S. Takahashi and W. Takahashi [Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515]. Therefore, by using the above result, an iterative algorithm for the solution of a optimization problem was obtained. [Copyright &y& Elsevier]

Abstract: Some sufficient and necessary conditions for the iterative sequence converging to a common fixed points for a family of nonexpansive mappings in Banach spaces are obtained. The results presented in this paper not only give an affirmative answer to Halpern''s open question and a partial answer to the Reich''s open question but also extend and improve some recent results of Bauschke [J. Math. Anal. Appl. 202 (1996) 150–159], Halpern [Bull. Amer. Math. Soc. 73 (1967) 957–961], Lions [C. R. Acad. Sci. Paris, Sér. A 284 (1977) 1357–1359], Reich [J. Math. Anal. Appl. 75 (1980) 128–292; PanAmer. Math. J. 4 (1994) 23–28], Shioji and Takahashi [Proc. Amer. Math. Soc. 125(12) (1997) 3641–3645], Takahashi et al. [J. Approximation Theory 91 (1997) 386–397; Sci. Math. Jap. 56(3) (2002) 417–422], Wittmann [Arch. Math. 58 (1992) 486–491] and Xu [Bull. Austral. Math. Soc. 65 (2002) 109–113; Commun. Appl. Nonlinear Anal. 10 (2003) 67–75]. As applications, at the end of the paper, we utilize our results to study the feasibility problem. [Copyright &y& Elsevier]

In this paper, we consider the equilibrium problem with finite number of families of players such that each family may not have the same number of players and finite number of families of constrained correspondences on the strategy sets. We also consider the case with two finite families of constrained correspondences on the strategies sets. We demonstrate an example of our equilibrium problem. We derive a fixed point theorem for a family of multimaps and a coincidence theorem for two families of multimaps. By using these results, we establish the existence of a solution of our equilibrium problems. The results of this paper generalize some known results in the literature. [Copyright &y& Elsevier]

In this paper, we define a generalized cyclic contraction and prove a unique fixed point theorem for these contractions. An illustrative example is given, which shows that these contraction mappings may admit the discontinuities and also that an existing result in the literature is effectively generalized by the theorem. We apply the fixed point result for generation of fractal sets through construction of an iterated function system and the corresponding Hutchinsion–Barnsley operator. The above construction is illustrated by an example. The study here is in the context of metric spaces.

In this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Prešić-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p, q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example.

In this paper, we prove some fixed point results for T-contraction mappings in partially ordered b-metric spaces, that generalize the main results of [H. Huang, S. Radenovič, J. Vujakovič, On some recent coincidence and immediate consequences in partially ordered b-metric spaces, Fixed Point Theory Appl., 2015, Paper No. 63]. As an application, we discuss the existence for a solution of a nonlinear integral equation.

In this paper we study topological and dynamical features of isolated invariant continua of continuous flows defined on surfaces. We show that near an isolated invariant continuum the flow is topologically equivalent to a C 1 flow. We deduce that isolated invariant continua in surfaces have the shape of finite polyhedra. We also show the existence of regular isolating blocks of isolated invariant continua and we use them to compute their Conley index provided that we have some knowledge about the truncated unstable manifold. We also see that the ring structure cohomology index of an isolated invariant continuum in a surface determines its Conley index. In addition, we study the dynamics of non-saddle sets, preservation of topological and dynamical properties by continuation and we give a topological classification of isolated invariant continua which do not contain fixed points and, as a consequence, we also classify isolated minimal sets. [ABSTRACT FROM AUTHOR]

Abstract: In this paper an existence theory is developed for first-order differential systems with coupled nonlocal conditions given by Stieltjes integrals. The approach is based on the fixed point theorems of Perov, Schauder and Schaefer and on a vector method for treating systems which uses matrices having spectral radius less than one. When the nonlocal conditions depend on functionals restricted to a proper subinterval, the nonlinear integral operator associated to the system splits into two parts, one of Fredholm type and another one of Volterra type. Correspondingly, the sufficient conditions for the existence results will differ in the two parts of the interval. Some examples are presented to illustrate the theory. [Copyright &y& Elsevier]

Abstract: Let be a uniformly convex and uniformly smooth Banach space. Let be an asymptotic pointwise nonexpansive mapping, where is a bounded, closed and convex subset of . In this paper we investigate conditions sufficient for the weak convergence of the generalized Mann and Ishikawa processes to a fixed point of . [Copyright &y& Elsevier]

Abstract: In this paper we present a simple and unified approach to the fixed point results on cone symmetric spaces and metric type spaces based on symmetric spaces fixed point theory. We also give a new characterization of semi-metric spaces with open balls. [Copyright &y& Elsevier]

Abstract: In this paper, the existence of a unique fixed point of a map satisfying a very general contractive condition on a suitable subset of a uniformly convex metric space is proved. This fixed point is approximated by averaging Krasnosel’skii iterations of a generalized nonexpansive map. Our results substantially improve and extend several known results existing in the literature. [Copyright &y& Elsevier]

In this paper, we study a fixed point problem for certain rational contractions on γ-complete metric spaces. Uniqueness of the fixed point is obtained under additional conditions. The Ulam–Hyers–Rassias stability of the problem is investigated. Well-posedness of the problem and the data dependence property are also explored. There are several corollaries of the main result. Finally, our fixed point theorem is applied to solve a problem of integral equation. There is no continuity assumption on the mapping.

In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-ofart. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process.

Abstract: In this paper, controllability for the system originating from semilinear functional differential equations in Hilbert spaces is studied. We consider the problem of approximate controllability of semilinear differential inclusion assuming that semigroup, generated by the linear part of the inclusion, is compact and under the assumption that the corresponding linear system is approximately controllable. By using resolvent of controllability Gramian operator and fixed point theorem, sufficient conditions have been formulated and proved. An example is presented to illustrate the utility and applicability of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we prove a strong convergence theorem of Halpern’s type for 2-generalized hybrid mappings in a Hilbert space. We also deal with strong convergence theorems by hybrid methods for these nonlinear mappings in a Hilbert space. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new concept of -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results. [Copyright &y& Elsevier]

Abstract: In this paper we deal with the existence of impulsive mild solutions for semilinear differential inclusions with nonlocal conditions, where the linear part generates an evolution system and the nonlinearity satisfies the lower Scorza–Dragoni property. Our theorems extend the existence propositions proved by Fan in 2010. An example is presented. [Copyright &y& Elsevier]

Abstract: In this paper, existence results are derived for the unique, smallest, greatest, minimal and maximal solutions of nonlinear distributional Cauchy problems. Dependence of solutions on the data is also studied. The obtained results are applied to impulsive differential equations. Main tools are fixed point results in function spaces and recently introduced concepts of regulated and continuous primitive integrals of distributions. [Copyright &y& Elsevier]

Abstract: In this paper, we prove existence, uniqueness and comparison results for solutions of differential and integral equations in Banach spaces containing Henstock–Kurzweil integrable functions from a compact real interval to an ordered Banach space. [Copyright &y& Elsevier]

Abstract: In this paper, we prove the existence and convergence of best proximity points for asymptotic cyclic contractions in metric spaces with the property UC, as well as for asymptotic proximal pointwise contractions in uniformly convex Banach spaces. Moreover, we consider a generalized cyclic contraction mapping and prove the existence of best proximity points for such a mapping in Banach spaces which do not necessarily satisfy the geometric property UC. [Copyright &y& Elsevier]

Abstract: In this paper, a general system of nonlinear variational inequality problem in Banach spaces was considered, which includes some existing problems as special cases. For solving this nonlinear variational inequality problem, we construct two methods which were inspired and motivated by Korpelevich’s extragradient method. Furthermore, we prove that the suggested algorithms converge strongly to some solutions of the studied variational inequality. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to establish DeMarr’s well-known theorem for an arbitrary family of symmetric Banach operator pairs in hyperconvex metric spaces without the compactness assumption. We also give necessary and sufficient criteria for the existence of a common fixed point of a semigroup of isometric mappings. As an application, several results on the invariant best approximation are proved. [Copyright &y& Elsevier]

Abstract: Let be a convex and compact subset of a space . In this paper, we consider the following iterative scheme for a one-parameter nonexpansive semigroup on : where and , and we prove that, under certain conditions, converges to a common fixed point of the semigroup . [Copyright &y& Elsevier]

Abstract: In this paper, we obtain some fixed and common fixed point theorems in finite dimensional normed Boolean vector spaces. Our results extend and unify some known results. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a condition on multivalued mappings which is a multivalued version of condition defined by Garcia-Falset et al. (2011) . It is shown here that some of the classical fixed point theorems for multivalued nonexpansive mappings can be extended to mappings satisfying this condition. Our results generalize the results in Lim (1974), Lami Dozo (1973), Kirk and Massa (1990), Garcia-Falset et al. (2011), Dhompongsa et al. (2009) and Abkar and Eslamian (2010)  and many others. [Copyright &y& Elsevier]

Abstract: In the present paper, we obtain a new KKM type theorem for intersectionally closed-valued KKM maps and some useful new basic consequences. Typical examples of them are abstract forms of Fan’s matching theorem, Fan’s geometric lemma, the Fan–Browder fixed point theorem, maximal element theorems, Fan’s minimax inequality, variational inequalities, and others. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence of pseudo-almost automorphic solutions of the semilinear integral equation in a Banach space , where , is the generator of an integral resolvent family of linear bounded operators defined on the Banach space , and is a pseudo-almost automorphic function. The main results are proved by using integral resolvent families combined with the theory of fixed points. [Copyright &y& Elsevier]

Abstract: Using an old M. Krein’s result and a result concerning symmetric spaces from [S. Radenović, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (1) (2011), 38–50], we show in a very short way that all fixed point results in cone metric spaces obtained recently, in which the assumption that the underlying cone is normal and solid is present, can be reduced to the corresponding results in metric spaces. On the other hand, when we deal with non-normal solid cones, this is not possible. In the recent paper [M.A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, 7 pages, Article ID 315398, doi:10.1115/2010/315398] the author claims that most of the cone fixed point results are merely copies of the classical ones and that any extension of known fixed point results to cone metric spaces is redundant; also that underlying Banach space and the associated cone subset are not necessary. In fact, Khamsi’s approach includes a small class of results and is very limited since it requires only normal cones, so that all results with non-normal cones (which are proper extensions of the corresponding results for metric spaces) cannot be dealt with by his approach. [Copyright &y& Elsevier]

Abstract: In the KKM theory, some authors adopt the concepts of the compact closure (ccl), compact interior (cint), transfer compactly closed-valued multimap, transfer compactly l.s.c. multimap, and transfer compactly local intersection property, respectively, instead of the closure, interior, closed-valued multimap, l.s.c. multimap, and possession of a finite open cover property. In this paper, we show that such adoption is inappropriate and artificial. In fact, any theorem with a term with “transfer” attached is equivalent to the corresponding one without “transfer”. Moreover, we can invalidate terms with “compactly” attached by giving a finer topology on the underlying space. In such ways, we obtain simpler formulations of KKM type theorems, Fan–Browder type fixed point theorems, and other results in the KKM theory on abstract convex spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we shall prove that some generalizations in fixed point theory are not real generalizations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the existence and uniqueness of (coupled) fixed points for mixed monotone mappings in partially ordered metric spaces with semi-monotone metric. As an application, we prove the existence and uniqueness of the solution for a first-order differential equation with periodic boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper is to prove the existence of a fixed point for a pointwise eventually nonexpansive mapping in a nearly uniformly convex Banach space. This provides an affirmative answer to a question given by Kirk and Xu [W.A. Kirk, Hong-Kun Xu, Asymptotic pointwise contraction, Nonlinear Anal. 69 (2008), 4706–4712]. [ABSTRACT FROM AUTHOR]

Abstract: In , Zamfirescu (1972) gave a fixed point theorem that generalizes the classical fixed point theorems by Banach, Kannan, and Chatterjea. In this paper, we follow the ideas of Dugundji and Granas to extend Zamfirescu’s fixed point theorem to the class of weakly Zamfirescu maps. A continuation method for this class of maps is also given. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper is to construct an Ishikawa type of hybrid algorithm for pseudo-contractive mappings in Hilbert spaces. Our results extend the recent ones announced by Yao et al. [Y.H. Yao, Y.C. Liou, G. Marino, A hybrid algorithm for pseudo-contractive mappings, Nonlinear Anal. 71 (2009) 4997–5002] and many others. [Copyright &y& Elsevier]

Abstract: The paper deals with the classical Caristi fixed point theorem in vector valued metric spaces. The results obtained seem to be new in this setting. [ABSTRACT FROM AUTHOR]