# Showing papers in "Nonlinear functional analysis and applications in 2014"

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TL;DR: In this paper, the authors describe all surjective gyrometric preserving maps on the threemodels of gyrovector spaces, the Einstein gyrogroup, the Mobius and the ProperVelocity.

Abstract: In this paper we describe all surjective gyrometric preserving maps on the threemodels of gyrovector spaces, the Einstein gyrogroup, the Mobius gyrogroup and the ProperVelocity gyrogroup.

17 citations

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TL;DR: In this paper, optimal control problem is addressed for distributed systems described by Cahn-Hilliard equation by the means of distributed control, initial control and Neumann boundary control, the existence and uniqueness is provided for weak solution using variational method.

Abstract: In this work, optimal control problem is addressed for distributed systems describedby Cahn-Hilliard equation by the means of distributed control, initial control andNeumann boundary control. The existence and uniqueness is provided for weak solutionusing variational method. Further, existence of optimal control is proved completely, andoptimality conditions is established for integral cost and quadratic cost, respectively. Lastly,Bang-Bang principle is deduced.

11 citations

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TL;DR: In this paper, the authors considered a class of convex functions in Opial-type integral inequalities and proved Cauchy type mean value theorems and used them in studying Stolarsky type means defined by the observed integral inequalities.

Abstract: In this paper we consider a certain class of convex functions in Opial-type integral inequalities. Cauchy type mean value theorems are proved and used in studying Stolarsky type means defined by the observed integral inequalities. A method of producing n-exponentially convex and exponentially convex functions is applied. Also, some new Opial-type equalities are given involving fractional integrals and fractional derivatives.

9 citations

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TL;DR: In this article, the authors give the sufficient condition of modified S-iteration process to converge to fixed point for asymptotically quasi-nonexpansive type mappings in the setting of CAT(0) space and also establish some strong convergence theorems of the said iteration process and mapping under suitable conditions.

Abstract: In this paper, we give the sufficient condition of modified S-iteration process to converge to fixed point for asymptotically quasi-nonexpansive type mappings in the setting of CAT(0) space and also establish some strong convergence theorems of the said iteration process and mapping under suitable conditions. Our results extend and improve many known results from the existing literature.

8 citations

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TL;DR: In this article, the authors prove local asymptotic stability results for a hybrid functional nonlinear fractional integral equation under weaker Lipschitz and compactness type conditions.

Abstract: We prove a couple of local asymptotic stability results for a hybrid functional nonlinear fractional integral equations under weaker Lipschitz and compactness type conditions. It is shown that comparable solutions of the considered hybrid functional nonlinear fractional integral equation are uniformly locally ultimately attractive and asymptotically stable on unbounded intervals of real line. We claim that our results are new and rely on ameasure theoretic fixed point theorem of Dhage (2014).

7 citations

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TL;DR: In this article, the existence of asymptotically stable solutions for a Volterra-Hammerstein integral equation in three variables is established via a fixed point theorem of Krasnosel'skii type, a condition for the relative compactness of a subset in certain space.

Abstract: Motivated by recent known results about the solvability of nonlinear functionalintegral equations in one, two or n variables, this paper establishes the existence of asymp-totically stable solutions for a Volterra-Hammerstein integral equation in three variables.The proofs are completed via a fixed point theorem of Krasnosel'skii type, a condition forthe relative compactness of a subset in certain space and integral inequalities with explicit estimates.

4 citations

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TL;DR: In this article, the authors study some fixed point theorems for self-mappings satisfying certain contraction principles on a convex complete metric space, and also improve and extend some very recently results in [9].

Abstract: In this paper we study some fixed point theorems for self-mappings satisfyingcertain contraction principles on a convex complete metric space. In addition, we also improve and extend some very recently results in [9].

4 citations

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TL;DR: In this paper, the existence and uniqueness of solutions for the neutral fractional integrodifferential equations with fractional integral boundary conditions with fixed point theorems was studied, where the fractional derivative considered here is in the Caputo sense.

Abstract: In this paper, we study the existence and uniqueness of solutions for the neutral fractional integrodifferential equations with fractional integral boundary conditions by usingfixed point theorems. The fractional derivative considered here is in the Caputo sense. Examples are provided to illustrate the results.

4 citations

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TL;DR: In this article, the multivalued weak contractions and weakly Picard operators on partial metric spaces were introduced and the Mizoguchi-Takahashi type fixed point theorem was given for multiivalued mappings.

Abstract: In the present paper, we introduce the multivalued weak contractions and the multivalued weakly Picard operators on partial metric space motivated by the metric spaceversion of these concepts given by Berinde and Berinde [14]. Then we give Mizoguchi-Takahashi type fixed point theorem for multivalued mappings on partial metric spaces. An illustrative example is also presented.

3 citations

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TL;DR: In this paper, the authors introduce several new generalized convolutions with a weight function for the Laplace, Fourier sine and Fourier cosine integral transforms for solving a class of integral equations.

Abstract: In this paper, we introduce several new generalized convolutions with a weight function for the Laplace, Fourier sine and Fourier cosine integral transforms. Convolution properties and their applications for solving a class of integral equations and systems of integral equations are presented.

2 citations

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Hebei University

^{1}TL;DR: In this paper, an iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the common fixed points of two asymptotically nonexpansive mappings in Hilbert spaces is introduced.

Abstract: In this paper, we introduce an iterative scheme for finding a common elementof the set of solutions of a generalized equilibrium problem and the set of common fixed points of two asymptotically nonexpansive mappings in Hilbert spaces. Weak and strongconvergence theorems are established for the iterative scheme.

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TL;DR: In this article, Chen and Guo gave a condition to converge to common fixed point of a finite-time iteration process with errors for two finite families of generalized asymptotically quasi-none-expansive mappings in the framework of Banach spaces.

Abstract: In this paper, we give a sucient condition to converge to common fixed point ofa nite step iteration process with errors for two finite families of generalized asymptotically quasi-nonexpansive mappings in the framework of Banach spaces. Also, we establish someweak and strong convergence theorems of the above said scheme and mappings using addi-tional assumptions to the space in the framework of uniformly convex Banach spaces. Theresults presented in this paper improve and extend some results of Chen and Guo (2011) [1], Sitthikul and Saejung (2009) [19] and many others.

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TL;DR: In this paper, a similar model was proposed for the propagation of high frequency electromagnetic waves in nonlinear dielectric media, and the existence, uniqueness, the asymptotic behavior and the expansion of the solution up to order N in a small parameter λ with error λ n+½ was proved.

Abstract: Motivated by the well-posedness results in [Nonlinear Anal. Ser. B: RWA. 4(3) (2003), 483, 501; Nonlinear Anal. Ser. B: RWA. 11(5) (2010), 3453-3462] for the models describing the propagation of high frequency electromagnetic waves in nonlinear dielectric media, because of their mathematical context, we study a similar model and prove results about existence, uniqueness, the asymptotic behavior and an asymptotic expansion of the solution up to order N in a small parameter λ with error λ^{N+½}

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TL;DR: In this paper, the exact explicit traveling wave solutions to the fKdV Sawada-Kotera equations are given by using a uniform method, and they obtained some new forms of the solutions more than that appeared in Wazwaz [9].

Abstract: In this paper the exact explicit traveling wave solutions to the fKdV Sawada-Kotera equations are given by using a uniform method. We obtained some new forms of the solutions more than that appeared in Wazwaz [9]. The results in this paper are significant extension.

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TL;DR: In this article, Chauhan et al. showed that subsequential continuity is independent of the notion of continuity or reciprocal continuity and showed that it is not a generalization of continuity.

Abstract: Recent results due to various authors (Chauhan et al.; Journal of Applied Math-ematics (2013), Beg and Chauhan; Novi Sad J. Math. (2013), Pant et al.; Advances in Fuzzy Systems (2013), Chauhan et al.; Vietnam Journal of Mathematics (2013), Rouzkard et al.;Bull. Belg. Math. Soc. Simon Stevin (2012), Imdad et al.; Appl. Math. Lett. (2011), Gopal and Imdad; Ann Univ Ferrara (2011) etc.) have been proved under the presumptionthat subsequential continuity is the generalization of continuity or reciprocal continuity. In this short note we communicate some important remarks about the concept of subsequential continuity and show that subsequential continuity is independent of the notion of continuityor reciprocal continuity.

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TL;DR: In this article, the authors present some coincidence and fixed point theo-rems for generalized contraction in partially ordered complete G-metric spaces, and give an existence and uniqueness for the solution of an initial-boundary-value problem.

Abstract: The purpose of this article is to present some coincidence and fixed point theo-rems for generalized contraction in partially ordered complete G-metric spaces. As an ap-plication, we give an existence and uniqueness for the solution of an initial-boundary-valueproblem. These results generalize and extend several well known results in the literature.

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TL;DR: Mahale and Nair as discussed by the authors used a modified center-type Lipschitz condition in their convergence analysis instead of using the standard standard condition, which was used in earlier studies such as Tautenhn (2002).

Abstract: In this paper, we expand the applicability of Lavrentiev regularization method forill-posed equations, recently presented in Mahale and Nair (2013). We use a modified center-type Lipschitz condition in our convergence analysis instead of Lipschitz-type condition usedin earlier studies such as Mahale and Nair (2000), (2013) and Tautenhn (2002).

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TL;DR: In this paper, the modified implicit Mann iteration process can be used to approximate the common fixed point of two strictly hemicontractive mappings in smooth Banach spaces, which is the case in this paper.

Abstract: The purpose of this paper is to prove that the modified implicit Mann iteration process can be applied to approximate the common fixed point of two strictly hemicontractive mappings in smooth Banach spaces.

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TL;DR: In this paper, the authors modify the proof of main theorem on the paper ''Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces'' ([3] and also confirm that they can convert non-normal cone to normal with constant one.

Abstract: In this paper we modify the proof of main theorem on the paper `Metrizabilityof Cone Metric Spaces Via Renorming the Banach Spaces' ([3]), and also we state and confirm that we can convert non-normal cone to normal with constant one. Therefore the metrizability of cone metric spaces via renorming the Banach spaces is possible. We also present an famous example herein.

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TL;DR: In this paper, a method was developed to reduce coupled fixed point problems in (ordered) metric and various generalized metric spaces to the respective results for mappings with one variable and applied to nonlinear Fredholm integral equations.

Abstract: In some recent papers, a method was developed of reducing coupled fixed point problems in (ordered) metric and various generalized metric spaces to the respective results for mappings with one variable. In this paper, we apply the mentioned method and obtain some coupled fixed point results for mappings satisfying φ-weak contractive conditions in ordered b-metric spaces. Examples show how these results can be used. Finally, an application to nonlinear Fredholm integral equations is presented, illustrating the e ectiveness of our generalizations.