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

Gyrometric preserving maps on einstein gyrogroups, mobius gyrogroups and proper velocity gyrogroups

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.

Optimal control of distributed parameter system given by cahn-hilliard equation

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.

More on certain Opial-type inequality for fractional derivatives and exponentially convex functions

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.

On the convergence of a modified s-iteration process for asymptotically quasi-nonexpansive type mappings in a cat(0) space

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.

Local attractivity and stability results for hybrid functional nonlinear fractional integral equations

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).

A nonlinear volterra-hammerstein integral equation in three variables

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.

Some results of fixed point theorems in convex metric spaces

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].

Existence results for neutral fractional integrodifferential equations with fractional integral boundary conditions

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.

Multivalued weakly picard operators on partial metric spaces

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.

The generalized convolutions with a weight function for laplace transform

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.

Convergence theorems for a generalized equilibrium problem and two asymptotically nonexpansive mappings in hilbert spaces

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.

Convergence of common fixed point of finite step iteration process for generalized asymptotically quasi-nonexpansive mappings

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.

A nonlinear wave equation associated with a nonlinear integral equation

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}

The uniform method to the solutions of type of the fifth-order sawada-kotera equations

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.

A critical remark on subsequential 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.

A generalization of geraghty's theorem in partially ordered g-metric spaces and application to ordinary differential equations

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.

Expanding the applicability of lavrentiev regularization methods for ill-posed equations under general source condition

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).

Implicit mann type iteration method involving two strictly hemicontractive mappings in banach spaces

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.

Possibility or impossibility of the metrizability of cone metric spaces via renorming the banach spaces

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.

COUPLED FIXED POINT THEOREMS FOR WEAKLY φ-CONTRACTIVE MIXED MONOTONE MAPPINGS IN ORDERED b-METRIC SPACES

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.