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In 2011, Jin Qinian has proposed a Levenberg–Marquardt method, by making use of duality mapping and the Bregman distance, to get an approximate solution of a nonlinear ill-posed operator equation in Banach space using an a posteriori parameter choice strategy and Morozov-type stopping rule. The method considered by Jin Qinian was an extension of the method proposed by M. Hanke in 1997 for the Hilbert space case. In this paper, we suggest a modified variant of the method, namely, the simplified Levenberg–Marquardt scheme in Banach spaces. The advantage of the method considered in the paper is that, it is also applicable for the operator equation with non-smooth operator. We establish convergence of the method under a modified a posteriori parameter choice strategy which is more feasible than the one considered by Jin Qinian (2011). Numerical example to demonstrate the validity of the considered method is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we study how to estimate the optimal dividend strategy in a discrete-time risk model with delayed claims. The insurance company pays dividends to shareholders, and each dividend is taxable. The company controls the dividend payments to maximize the expectation of accumulated discounted dividends after tax prior to ruin. This paper aims to develop a method to estimate the optimal dividend strategy by using historical data directly. For the purpose we construct a nonlinear stochastic operator on the space l ∞ , which is proved to have contraction property. Fortunately the stochastic fixed point of the operator converges to a real sequence in probability, from which a consistent estimator of the optimal strategy follows. This is an important advantage of the stochastic operator method because the consistency property is difficult to be obtained by traditional methods with estimated distributions for claims. Finally, the method is applied in an example. The estimation results by using simulation data show that the optimal dividend strategy is a conditional threshold strategy, and the optimal dividend threshold tends to be stable with the sample size increasing. [ABSTRACT FROM AUTHOR]

Mahale and Nair (2009) considered a iterated Lavrentive regularization method for obtaining stable approximate solution of nonlinear ill-posed operator equation F(x) = y, where F : D (F) ⊂ X → X is a nonlinear monotone operator on Hilbert space X. In this paper, we do convergence analysis of the method under the weaker non-linearity condition than the one considered by Mahale and Nair. We obtain convergence and rate of convergence results for the method merely under Lipschitz's condition. At the end of the paper, we give a numerical example to demonstrate our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and q-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of the initial-nonlinear nonlocal solutions for a parabolic system in a weighted Sobolev space. The methods applied are the Faedo–Galerkin approximation and the general theory of weak compactness in appropriate weighted Sobolev spaces together with using the Poincaré-type operator for dealing nonlinear nonlocal conditions. Furthermore, the boundedness and positivity of solutions depending on the boundedness and positivity of given data are also discussed by using suitable test functions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Newton-iteration scheme based on Galerkin and multi-Galerkin operators to solve non-linear integral equations of the Fredholm-Hammerstein type for both smooth and weakly singular algebraic and logarithmic type kernels. By choosing X n as space of piecewise polynomials subspace of degree ≤ r − 1 , we show that for a smooth kernel, Galerkin and multi-Galerkin approximate solution in the kth Newton-iteration scheme converges with the orders O (h (k + 1) r) and O (h (2 k + 3) r) , respectively, where h is the norm of the partition. For weakly singular kernels, we show that the Galerkin approximate solution in the kth Newton-iteration scheme converges with the orders O (h r + k (1 − α)) , 0 < α < 1 for algebraic kernels and O (h r + k (log ⁡ h) k) for logarithmic kernels. Also the multi-Galerkin approximate solution in the kth Newton-iteration scheme converges with the orders O (h r + (k + 1) (1 − α)) for algebraic kernels and O (h r + k + 1 (log ⁡ h) k + 1) for logarithmic kernels. Numerical results are given for the justification of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we provide an alternative proof of the separation theorem, which can be easily extended to a certain class of systems of elliptic and parabolic nonlinear equations in non-reflexive spaces. [ABSTRACT FROM AUTHOR]

In the present paper, convergence in modular spaces is investigated for a class of nonlinear discrete operators, namely the nonlinear multivariate sampling Kantorovich operators. The convergence results in the Musielak-Orlicz spaces, in the weighted Orlicz spaces, and in the Orlicz spaces follow as particular cases. Even more, spaces of functions equipped by modulars without an integral representation are presented and discussed. [ABSTRACT FROM AUTHOR]

We consider a mixed variational problem governed by a nonlinear operator and a set of constraints. Existence, uniqueness and convergence results for this problem have already been obtained in the literature. In this current paper we complete these results by proving the well-posedness of the problem, in the sense of Tykhonov. To this end we introduce a family of approximating problems for which we state and prove various equivalence and convergence results. We illustrate these abstract results in the study of a frictionless contact model with elastic materials. The process is assumed to be static and the contact is with unilateral constraints. We derive a weak formulation of the model which is in the form of a mixed variational problem with unknowns being the displacement field and the Lagrange multiplier. Then, we prove various results on the corresponding mixed problem, including its well-posedness in the sense of Tykhonov, under various assumptions on the data. Finally, we provide mechanical interpretation of our results. [ABSTRACT FROM AUTHOR]

This paper considers the approximate controllability for a class of abstract semilinear control systems using a method called surjectivity theorems for nonlinear operator equations under restrictive assumptions. The sufficient conditions for approximate controllability are derived under the natural assumptions on the nonlinear terms, which is an odd homogeneous and the nonlinear inverse considered as a multivalued mapping is bounded. An example is given to illustrate our main results. [ABSTRACT FROM AUTHOR]

This paper focuses on the following degenerate parabolic equation u t − d i v (σ (x) | ∇ u | p − 2 ∇ u) + f (x , u) = g i n Ω × R + , u = 0 o n ∂ Ω × R + , u (x , 0) = u 0 (x) i n Ω , where Ω is a smooth bounded domain in R N , (N ≥ 2) , 1 < p < N , u 0 , g ∈ L 1 (Ω) , σ (x) is positive almost everywhere and satisfies proper degenerate conditions. The existence and uniqueness result is proved in the framework of entropy solutions. For the long-time behavior, we prove the existence of a global attractor in L q (Ω) by using some delicate estimates on the solution, which are derived by taking advantage of both the leading operator and the zero-order nonlinear term. The aforementioned results improve some previous results in the literature in several aspects. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for noncoercive mixed equilibrium problems which are described by the sum of a maximal monotone bifunction and a pseudomonotone (or quasimonotone) bifunction in the sense of Brézis. Our approach is based on recession analysis and on recent results established by the authors for the existence of solutions of mixed equilibrium problems under pseudomonotone perturbations. As an application, we study the existence of solutions for nonlinear evolution equations associated with a noncoercive time-dependent pseudomonotone (or quasimonotone) operator. [ABSTRACT FROM AUTHOR]

This paper investigates the sliding mode control (SMC) problem for a class of delta operator uncertain time-delay nonlinear systems through Takagi–Sugeno fuzzy models. Some new sufficient conditions for asymptotic stability analysis of the sliding motion are obtained in terms of linear matrix inequalities with some convexification techniques. Then two new dynamic SMC design methods are synthesised to force the resulting closed-loop system states onto the sliding surface in finite time. Two simulation examples are finally given to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the approximate controllability for semi-linear retarded functional integro-differential equations by using the Fredholm theory in Hilbert spaces. We no longer require the compactness of structural operators to obtain the approximate controllability for the nonlinear differential system, but instead we use the theory of interpolation spaces and the regularity of solutions of semi-linear given equations with unbounded principal operators. Finally, based on the properties of general degree theory in infinite dimensional spaces, we investigate the relation between the reachable set of trajectories of the semi-linear retarded functional integro-differential system and that of its corresponding linear system excluded by the nonlinear term. [ABSTRACT FROM AUTHOR]

In this paper, the optimal dividend problem in a discrete-time risk model with interest is discussed. Assume that the premium received per unit time is a positive real-valued random variable, and the sequence of premiums is a Markov chain owing to the environmental effects. In arbitrary unit time whether a claim occurs or not is related to the premium received in the corresponding period. Under the constraint of a given survival probability, the optimal control strategy for dividends paid periodically to the shareholders is considered. We provide some properties and an algorithm for the optimal control strategy by structuring a non-linear operator and applying the fixed point theorem. Numerical examples are presented to illustrate the algorithm. [ABSTRACT FROM AUTHOR]

In this paper we study existence, nonexistence and classification of radial positive solutions of some weighted fully nonlinear equations involving Pucci extremal operators. Our results are entirely based on the analysis of the dynamics induced by an autonomous quadratic system which is obtained after a suitable transformation. This method allows to treat both regular and singular solutions in a unified way, without using energy arguments. In particular we recover known results on regular solutions for the fully nonlinear non weighted problem by alternative proofs. We also slightly improve the classification of the solutions for the extremal operator M −. [ABSTRACT FROM AUTHOR]

In the present paper, we study infinite dimensional orthogonality preserving the second-order nonlinear Markov operators. It is proved that subjectivity of the second-order nonlinear Markov operators is equivalent to the orthogonality preserves in the class of π-Volterra operators. Moreover, a full description of such kind of operators has been found in terms of heredity coefficients. Besides, we are able to represent these operators their canonical forms. Furthermore, some properties of orthogonality preserving the second-order nonlinear operators and their fixed points are studied. [ABSTRACT FROM AUTHOR]

This paper deals with blow-up and quenching solutions of degenerate parabolic problem involving m-Laplacian operator and nonlinear boundary flux. The blow-up and quenching criteria are classified under the conditions on the initial data but with less conditions on the relationship among the exponents, respectively. Moreover, asymptotic properties including singular rates, set and time estimates are determined for the blow-up solutions and the quenching solutions, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we study the structure of finite dimensional estimation algebras with state dimension 3 and rank 2 arising from a nonlinear filtering system by using the theories of the Euler operator and under-determined partial differential equations. It is proved that if the estimation algebra contains a degree two polynomial, then the Wong Ω-matrix must be a constant matrix. Moreover, all functions in the estimation algebra must be linear functions. [ABSTRACT FROM AUTHOR]

In this paper we study the strong maximum principle for equations of the form F [ u ] = H (u , | D u |) where F is either a fully nonlinear elliptic operator or is the p-Laplace operator. We give sufficient conditions on H to ensure that the strong maximum principle (SMP) holds. The condition is also necessary for SMP to hold for the the equation F [ u ] = g (| D u |). [ABSTRACT FROM AUTHOR]

In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new family of nonlinear schemes conserve the numerical properties of the linear schemes, such as the L 1 -stability, the order of accuracy or compression rate but avoiding Gibbs phenomenon close to the discontinuities. The generalized harmonic mean was introduced in the framework of point-values in [A. Guessab, M. Moncayo, and G. Schmeisser, A class of nonlinear four-point subdivision schemes. Properties in terms of conditions, Adv. Comput. Math. 37 (2012), pp. 151–190] in order to improve the results of the harmonic mean. However, in the cell-average setting our conclusion is that, from a numerical point of view, the advantage of using the new mean is not clear. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a class of semilinear differential variational systems with nonlocal boundary conditions, which are obtained by mixing semilinear evolution equations and generalized variational inequalities. First we prove essential properties of the solution set for generalized variational inequalities. Then without requiring any compactness condition for the evolution operator or for the nonlinear term, two existence results for mild solutions are established by applying a weak topology technique combined with a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, the partialS-controllability of semilinear partially observable control systems is investigated. The essence of study is the presence of partial observations. We define a weakened partialS-controllability concept for partially observable systems. A sufficient condition for this controllability concept is proved. The method of proof differs from the traditional proofs by fixed-point theorems. The obtained result is demonstrated with examples. [ABSTRACT FROM PUBLISHER]

In this paper, we study fixed point proximity algorithms for a TVL1 restoration model recovering blurred images with impulsive noise, and image inpainting. The model that minimizes the sum of a data fidelity term in theℓ¹-norm, a term in ℓ²-norm and total-variation regularization term is strictly convex. We obtain the solution of the model through finding a fixed point of a nonlinear mapping expressed in terms of the proximity operator of the ℓ¹-norm or the ℓ²-norm, each of which is explicitly given. The non-expansivity of the mapping is also analysed theoretically. This formulation naturally leads to fixed-point algorithms for numerical treatment of the model. Numerical experiments demonstrate that the proposed algorithms perform favourably. [ABSTRACT FROM AUTHOR]

In this paper, we prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of a finite family of variational inclusion problems in Hilbert spaces. Moreover, we utilize our main result to fixed point problems of various nonlinear mappings and the set of solutions of variational inclusion problems. [ABSTRACT FROM AUTHOR]

The present paper is concerned with a nonlinear partial differential control system arising in phase transition modelling. The control constraint is given by a state-dependent nonconvex-valued multivalued mapping. We study the problem of minimisation of a given integral cost functional over solutions to the above system. The cost integrand is nonconvex in the control variable. Relaxation results of Bogolyubov-type are obtained for this problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose some sufficient conditions to obtain the existence of common fixed points for a pair of self-mappings satisfying Lipschitz-type conditions in noncomplete metric space. Our results improve and extend the results of Pant [Common fixed points of Lipschitz-type mapping pairs,J. Math. Anal. Appl.240, (1999), 280–283] and Khan et al. [Coincidences of Lipschitz-type hybrid maps and invariant approximation, Numer. Funct. Anal. Optim. 28(9–10), (2007), 1165–1177]. As an application of our results we solve an eigenvalue problem for operators defined on a normed space. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the equation |∇u|αℳa, A(D2u) = −f(u) in a bounded smooth domain Ω, with both Dirichlet conditionu = 0 and Neumann condition, wherecis a constant, α > −1,uis of constant sign and ℳa, Ais one of the Pucci operator. We prove, for different nonlinearitiesf, that, whenais sufficiently close toA, eitheru = c = 0 = f(0) or Ω is a ball,uis radial, andc ≠ 0 in Ω. [ABSTRACT FROM AUTHOR]

The existence of at least three positive solutions to three-point boundary conditions for second-order impulsive differential equations with deviating arguments is discussed in this paper. Deviating arguments may be of advanced or delayed types. To obtain the results the Leggett-Williams fixed point is applied [R. W. Leggett and L. R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana Univ. Math. J. 28 (1979), pp. 673-688.]. An example is added to verify the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the strong convergence of the hybrid steepest descent method relative to the case when the involved operators belong to a wide class of possibly nonself-mappings. Our convergence results cover previous ones, and the techniques of analysis used are simple and can be adapted to many other fixed point methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose two new derivative-free algorithms for nonlinear equations. The first is based on quasi-Newton method and is globally and superlinearly convergent under some mild assumptions. The second combines the ideas of the first with the filter strategy, which helps to reduce the backtracking steps in calculating the stepsizes, for evaluating candidate points. We show its convergence under the same assumptions. The resulting algorithms show some attractive features. Some encouraging preliminary computational results for both algorithms are reported. [ABSTRACT FROM AUTHOR]

Many commonly used models for the fundamental image processing task of noise removal can deal with Gaussian white noise. However, such Gaussian models are not effective in restoring images with Poisson noise, which is ubiquitous in certain applications. Recently, Le-Chartrand-Asaki derived a new data-fitting term in the variational model for Poisson noise. This paper proposes a multilevel algorithm for efficiently solving this variational model. As expected of a multilevel method, it delivers the same numerical solution many orders of magnitude faster than the standard single-level method of coordinate descent time-marching. Supporting numerical experiments on 2D gray scale images are presented. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the weak and strong convergence of an implicit iteration process to a common fixed point for two finite families of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Xu and Ori, Numer. Funct. Anal. Optim. 2001; 22:767-773, Zhou and Chang, Numer. Fund. Anal. Optim. 2002; 23:911-921, Chidume and Shahzad, Nonlinear. Anal. 2005; 62: 1149-1156. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of solutions of a more general class of stochastic functional integral equations. The main tools here are the measure of noncompactness and the fixed point theorem of Darbo type. The results of this paper generalize the results of Rao–Tsokos [Rao, A.N.V.; Tsokos, C.P. A class of stochastic functional integral equations. Coll. Math. 1976, 35, 141–146.] and Szynal–Wedrychowicz [Szynal, D.; Wedrychowicz, S. On existence and an asymptotic behaviour of random solutions of a class of stochastic functional integral equations. Coll. Math. 1987, 51, 349–364.]. [ABSTRACT FROM AUTHOR]

This paper proposes fundamentals for stability and success of a global system composed by a mobile robot, a real environment and a navigation architecture with time constraints. Contraction theory is a typical framework that provides tools and properties to prove the stability and convergence of the global system to a unique fixed point that identifies the mission success. A stability indicator based on the combination contraction property is developed to identify the mission success as a stability measure. The architecture is fully designed throughC1nonlinear dynamical systems and feedthrough maps, which makes it amenable for contraction analysis. Experiments in a realistic and uncontrolled environment are realised to verify if inherent perturbations of the sensory information and of the environment affect the stability and success of the global system. [ABSTRACT FROM AUTHOR]

The present paper deals with a nonlinear boundary value problem derived from a model introduced by Rotenberg describing the growth of a cell population. Each cell of this population is distinguished by its degree of maturityand its maturation velocity. The biological boundary atandare fixed and tightly coupled through the mitosis. We present existence results for the problem in the case daughter cells and mother cells are related by a general reproduction rule and the maturation velocity is allowed to be infinite, i.e.. Our results are based on the classical topological fixed point theorems and use a compactness result established by below. [ABSTRACT FROM AUTHOR]

The paper presents a vectorial approach for coupled general nonlinear Schrödinger systems with nonlocal Cauchy conditions. Based on fixed-point principles, the use of matrices with spectral radius less than one, and on basic properties of the Schrödinger solution operator, several existence results are obtained. The essential role of the support of the nonlocal Cauchy condition is emphasized and fully exploited. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the existence of such periodic solutions. [ABSTRACT FROM AUTHOR]

The modal-calculus extends basic modal logic with second-order quantification in terms of arbitrarily nested fixpoint operators. Its satisfiability problem is EXPTIME-complete. Decision procedures for the modal-calculus are not easy to obtain though since the arbitrary nesting of fixpoint constructs requires some combinatorial arguments for showing the well-foundedness of least fixpoint unfoldings. The tableau-based decision procedures so far also make assumptions on the unfoldings of fixpoint formulas, e.g., explicitly require formulas to be in guarded normal form. In this paper we present a tableau calculus for deciding satisfiability of arbitrary, i.e., not necessarily guarded-calculus formulas. It is based on a new unfolding rule for greatest fixpoint formulas which allows unguarded formulas to be handled without an explicit transformation into guarded form, thus avoiding a (seemingly) exponential blow-up in formula size. We prove soundness and completeness of the calculus, and compare it empirically to using guarded transformation instead. The new unfolding rule can also be used to handle nested star operators in PDL formulas correctly. [ABSTRACT FROM AUTHOR]

In this study, approximation properties of the Mellin-type nonlinear integral operators defined on multivariate functions are investigated. In order to get more general results than the classical aspects, we mainly use the summability methods defined by Bell. Considering the Haar measure with variation semi-norm in Tonelli's sense, we approach to the functions of bounded variation. Similar results are also obtained for uniformly continuous and bounded functions. Using suitable function classes we investigate the rate of convergence in the approximation. Finally, we give a non-trivial application verifying our approach. [ABSTRACT FROM AUTHOR]

I will describe some results on the dynamics of the renormalization operator in the spaces of interval dynamical systems and some of the fundamental tools. This paper is related to my talk at the conference ‘Dynamics and Applications’, in honour of David Rand and Mauricio Peixoto, from 8 to 12th of September 2008, at the University of Minho, Braga. [ABSTRACT FROM PUBLISHER]

In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear operators exists in the framework of viscosity solutions. Here we want to show that for the radially symmetric operators or in the one dimensional case a much simpler theory, based on ode and degree theory arguments, can be established. We obtain the complete set of eigenvalues and eigenfunctions characterized by the number of zeroes. [ABSTRACT FROM AUTHOR]

In this paper, we prove three strong convergence theorems of modified Mann iteration for relatively asymptotically nonexpansive mappings, relatively nonexpansive mappings, and maximal monotone operators in a Banach space, respectively. Our results extend and improve the recent ones announced by Nakajo, Takahashi, Matsushita, Kim, Martinez-Yanex, Xu, and some others. [ABSTRACT FROM AUTHOR]

For problems that are aimed at obtaining a common fixed point of a countable class ( T i ) i &Element; I of operators by an iterative procedure, usually an important role is played by an inequality that expresses the behavior of the distances of the original points x and their images T i x to the common fixed point set. The different inequalities that have appeared in the literature seem to impose a classification of the operators in two types; we propose a hierarchical description of the classes belonging to each type, based on some non-negative parameter. This hierarchical presentation makes it easier to investigate (existing or new) results concerning iterative procedures with respect to the possibility of broadening their scope of applicability. [ABSTRACT FROM AUTHOR]

The paper discusses common fixed point theory for generalized I -contractions of Ciric and R -subweakly commuting maps. Various results on invariant approximations are obtained. [ABSTRACT FROM AUTHOR]

Some stationary and nonstationary projection-iteration methods for a wide class of nonlinear operators are studied. Strong and weak convergence theorems are established. A generalized Edelstein's fixed point theorem is stated. By means of this theorem and of the studied methods one can solve approximately a number of nonlinear operator equations for which the usual Picard method is not applicable. *This paper was supported by the National Fundamental Research Program in Natural Science of Vietnam. [ABSTRACT FROM AUTHOR]

Let f be a fixed point free increasing continuous function of the interval into itself such that exists, does not depend on x and belongs to the interval (0, 1). We deal with the Schröder equation in a more general setting by giving necessary and sufficient conditions for it to have a solution which is uniformly regularly varying with respect to (f, a) for some , that is, the relation holds locally uniformly with respect to for some . We show that such a solution is continuous, increasing and regularly varying in the usual sense. [ABSTRACT FROM AUTHOR]

We consider the problem of characterizing feasible locations for identical facilities in a tree network when lower bound constraints are imposed on distances between the facilities as well as between each fixed point and the facilities. We first eliminate from the network some fixed points whose associated constraints are redundant, and then develop a sequential procedure for locating the maximum number of facilities. We relate this maximum number to the consistency of the distance constraints; the resulting information is relevant in solving a certain class of location problems on tree networks. [ABSTRACT FROM AUTHOR]

Let { A i , E i } be the elliptic complex on an n-dimensional smooth closed Riemannian manifold X with the first-order differential operators A i and smooth vector bundles E i over X. We consider nonlinear operator equations, associated with the parabolic differential operators ∂ t + Δ i , generated by the Laplacians Δ i of the complex { A i , E i } , in special Bochner–Sobolev functional spaces. We prove that under reasonable assumptions regarding the nonlinear term the Frechét derivative A i ′ of the induced nonlinear mapping is continuously invertible and the map A i is open and injective in chosen spaces. [ABSTRACT FROM AUTHOR]

Our goal in this paper is to present three classes of cyclic (α, β)-(ψ, θ, φ)-admissible multivalued mappings, and then prove the existence of fixed point in a complete metric space. Our results generalize and extend several works. Two examples were added to support our work. [ABSTRACT FROM AUTHOR]