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Positive solutions of fractional integral equations by the technique of measure of noncompactness

Agarwal 2 Manuel De la Sen 0 0 Institute of Research and Development of Processes IIDP Faculty of Science and Technology, University of the Basque Country , Leioa , Spain 1 Department of Mathematics, Sari

New ergodic convergence theorems for non-expansive mappings and m-accretive mappings

Two new ergodic convergence theorems for approximating the common element of the set of zero points of an m-accretive mapping and the set of fixed points of an infinite family of non-expansive mappings in a real smooth and uniformly convex Banach space are obtained, which improves some of the previous work. The computational experiments to demonstrate the effectiveness of the...

Generalizations of Sherman’s inequality by Lidstone’s interpolating polynomial

In majorization theory, the well-known majorization theorem plays a very important role. A more general result was obtained by Sherman. In this paper, concerning 2n-convex functions, we get generalizations of these results applying Lidstone’s interpolating polynomials and the Čebyšev functional. Using the obtained results, we generate a new family of exponentially convex...

Lyapunov type inequalities for even order differential equations with mixed nonlinearities

In the case of oscillatory potentials, we present Lyapunov and Hartman type inequalities for even order differential equations with mixed nonlinearities: x ( 2 n ) ( t ) + ( − 1 ) n − 1 ∑ i = 1 m q i ( t ) | x ( t ) | α i − 1 x ( t ) = 0 , where n , m ∈ N and the nonlinearities satisfy 0 < α 1 < ⋯ < α j < 1 < α j + 1 < ⋯ < α m < 2 . MSC: 34C10.

A short note on C ∗ -valued contraction mappings

In this short note we point out that the recently announced notion, the C ∗ -valued metric, does not bring about a real extension in metric fixed point theory. Besides, fixed point results in the C ∗ -valued metric can be derived from the desired Banach mapping principle and its famous consecutive theorems.

Strong convergence theorems of general split equality problems for quasi-nonexpansive mappings

The purpose of this paper is to introduce and study the general split equality problem and general split equality fixed point problem in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions, we prove that the sequences generated by the proposed new algorithm converges strongly to a solution of the general split equality fixed point problem and the general...

Convergence theorems of convex combination methods for treating d-accretive mappings in a Banach space and nonlinear equation

Agarwal 1 2 0 School of Mathematics and Statistics, Hebei University of Economics and Business , Shijiazhuang, 050061 , China 1 Department of Mathematics, Faculty of Science, King Abdulaziz University

Fixed-point theorems for nonlinear operators with singular perturbations and applications

In this paper, using fixed-point index theory and approximation techniques, we consider the existence and multiplicity of fixed points of some nonlinear operators with singular perturbation. As an application we consider the existence and multiplicity of positive solutions of singular systems of multi-point boundary value problems, which improve the results in the literature.

Constructed nets with perturbations for equilibrium and fixed point problems

In this paper, an implicit net with perturbations for solving the mixed equilibrium problems and fixed point problems has been constructed and it is shown that the proposed net converges strongly to a common solution of the mixed equilibrium problems and fixed point problems. Also, as applications, some corollaries for solving the minimum-norm problems are also included.MSC...

On coupled fixed point results in asymmetric G-metric spaces

Using a combination of techniques introduced by Jleli and Samet (Fixed Point Theory Appl. 2012:210, 2012) and Samet et al. (Int. J. Anal. 2013:917158, 2013) on the one hand, and by Kadelburg et al. (Bull. Math. Anal. Appl. 4:51-63, 2012) on the other hand, we show that several coupled fixed point results in (ordered) G-metric spaces obtained recently are simple consequences of...

The well-posedness for a system of generalized quasi-variational inclusion problems

We introduce the concept of Levitin-Polyak well-posedness for a system of generalized quasi-variational inclusion problems and show some characterizations of Levitin-Polyak well-posedness for the system of generalized quasi-variational inclusion problems under some suitable conditions. We also give some results concerned with the Hadamard well-posedness for the system of...

Properties of solutions of fourth-order differential equations with boundary conditions

In this paper, we establish some sufficient conditions for ( 2 , 2 ) -disconjugacy and study the distribution of zeros of nontrivial solutions of fourth-order differential equations. The results are extended to cover some boundary value problems in bending of beams. The main results are proved by making use of a generalization of Hardy’s inequality and some Opial-type...

On q-analogue of a complex summation-integral type operators in compact disks

Recently, Gupta and Wang introduced certain q-Durrmeyer type operators of real variable x ∈ [0, 1] and studied some approximation results in the case of real variables. Here we extend this study to the complex variable for analytic functions in compact disks. We establish the quantitative Voronovskaja type estimate. In this way, we put in evidence the over convergence phenomenon...

Strong convergence theorems for equilibrium problems and weak Bregman relatively nonexpansive mappings in Banach spaces

In this paper, a shrinking projection algorithm based on the prediction correction method for equilibrium problems and weak Bregman relatively nonexpansive mappings is introduced and investigated in Banach spaces, and then the strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some...

Duality for semi-infinite programming problems involving ( H p , r ) -invex functions

The present paper is framed to study weak, strong and strict converse duality relations for a semi-infinite programming problem and its Wolfe and Mond-Weir-type dual programs under generalized (Hp,r)-invexity.MSC: 90C32, 49K35, 49N15.

Inequalities for Green's operator applied to the minimizers

In this paper, we prove both the local and global Lφ -norm inequalities for Green's operator applied to minimizers for functionals defined on differential forms in Lφ -averaging domains. Our results are extensions of Lp norm inequalities for Green's operator and can be used to estimate the norms of other operators applied to differential forms. 2000 Mathematics Subject...

New upper bounds of n!

In this article, we deduce a new family of upper bounds of n! of the form n ! < 2 π n ( n / e ) n e M n [ m ] n ∈ ℕ , M n [ m ] = 1 2 m + 3 1 4 n + ∑ k = 1 m 2 m - 2 k + 2 2 k + 1 2 - 2 k ζ ( 2 k , n + 1 / 2 ) m = 1 , 2 , 3 , . . . . We also proved that the approximation formula 2 π n ( n / e ) n e M n [ m ] for big factorials has a speed of convergence equal to n -2m-3 for m = 1...

Nonlinear -Fuzzy stability of cubic functional equations

Journal of Inequalities and Applications Nonlinear L-Fuzzy stability of cubic functional equations Ravi P Agarwal agarwal@tamuk 0 Yeol Je Cho Reza Saadati Shenghua Wang 0 Department of Mathematics

Duality in nondifferentiable minimax fractional programming with B-(p, r)-invexity

. Acknowledgements Izhar Ahmad thanks the King Fahd University of Petroleum and Minerals for the support under the Fast Track Project no. FT100023. Ravi P. Agarwal gratefully acknowledges the support provided by the

Stability analysis for parametric generalized vector quasi-variational-like inequality problems

In this article, we consider a class of parametric generalized vector quasi-variational-like inequality problem (for short, (PGVQVLIP)) in Hausdorff topological vector spaces, where the constraint set K and a set-valued mapping T are perturbed by different parameters, and establish the nonemptiness and upper semicontinuity of the solution mapping S for (PGVQVLIP) under some...