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In this paper, the generalizations of Gronwall?s type integral inequalities with singular kernels are established. In applications, theorems on stability estimates for the solutions of the nonliner integral equation and the integral-differential equation of the parabolic type are presented. Moreover, these inequalities can be used in the theory of fractional differential equations.

‎I‎n‎ ‎this‎ ‎paper‎, ‎w‎‎e study the existence of weak solutions for ‎stationary‎‎ fractional reaction-diffusion ‎equations‎‎ ‎with‎ ‎Riemann‎-‎Liouville‎ boundary ‎conditions‎. An‎ appropriate fractional ‎Hilbert‎ space ‎is‎ introduced and a compact embedding theorem demonstrated. ‎Existence results are established using generalized Weierstrass theorem and relatively simple techniques from nonlinear functional analysis‎.

In this paper, we consider an inverse elliptic problem with Neumann type overdetermination and construct a fourth order of accuracy difference scheme for its solution. Stability, almost coercive stability and coercive stability estimates for the solution of difference problem are proved. Later, we construct a fourth order difference scheme for an inverse problem for multidimensional elliptic equation with Neumann type overdetermination and Dirichlet boundary condition. Finally, we illustrate numerical example with descriptions of numeric realization in a two-dimensional case. WOS:000397270800008 2-s2.0-85014474030

In this paper, based on some biological meaning, triple-negative T cells (TN) and the immature singlepositive T cells (CD3^{−}4^{+}8^{−} and CD3^{−}4^{−}8^{+}) have been introduced into well known Mehr’s non-linear differential equation which is used to describe proliferation, differentiation and death of T cells in the thymus (Modeling positive and negative selection and differentiation processes in the thymus, Journal of Theoretical Biology, 175 (1995) 103-126), and a class of improved nonlinear differential system with seven state variables and time delays has been proposed. Then, by using quasi-steady-state approximation and some classical analysis techniques of functional differential equations, the local and global asymptotic stability of the equilibrium of the system have been analysed. Finally, some numerical simulations are given to summarize the applications of the theoretical results.

In this paper we define the tangential property in partial metric spaces to prove a common fixed point theorems for two pairs of self mappings, which satisfying a generalized weak contractive condition as well as satisfying a generalized contraction, an example is given to illustrate ours results.

In this paper, we obtain some new fixed point theorems for (?,?,?,?) -contractive multi-valued mappings in ?-?-T-complete Menger PM-spaces, which turn out to generalize many results in existing literatures. Some examples are also given to illustrate the definition and support our new results. Moreover, some interesting fixed point results endowed with binary relations or graphs are derived as applications of our main results.

In this paper, we first prove existence of fixed points of generalized nonexpansive mappings in CAT(0) spaces. These are the mappings which satisfy the so-called condition (E). We then approximate them by the ?-convergence and strong convergence using Picard-Mann hybrid iterative process. Our results generalize the corresponding results of many authors.

WOS:000397270800014 In this paper, we investigate the extremal solutions for a class of nonlinear fractional differential equations with order q is an element of (0; 1) by means of monotone iterative technique via initial time different coupled upper and lower solutions.

In this paper, we investigate scattering theory of the impulsive Sturm-Liouville boundary value problem (ISBVP). In particular, we find the Jost solution and the scattering function of this problem. We also study the properties of the Jost function and the scattering function of this ISBVP. Furthermore, we present two examples by getting Jost function and scattering function of the impulsive boundary value problem. Besides, we examine the eigenvalues of these boundary value problems given in examples in detail.

In this paper, some fixed point results of Ciric type in partial b-metric spaces are complemented and generalized. An example is given to support the obtained results.

In the present paper, we introduce the notion of ?-type F-?-contraction and establish related fixed point results in metric spaces. An example is also given to illustrate our main results and to show that our results are proper generalization of Altun et al. (2015), Miank et al. (2015), Altun et al. (2016) and Olgun et al. (2016). We also obtain fixed point results in the setting of partially ordered metric spaces. Finally, an application is given to set up the existence of positive definite solution of non-linear matrix equation.

iscan, imdat/0000-0001-6749-0591 WOS: 000428735200005 In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

In this paper, we establish some fixed point theorems in G-metric spaces involving generalized cyclic contractions. Some subsequent results are derived. The presented results generalize many well known results in the literature. Moreover, we provide some concrete examples and an application on the existence and uniqueness of solutions to a class of nonlinear integral equations.

In this paper, we present some sufficient conditions for which a Banach space has normal structure and therefore the fixed point property for nonexpansive mappings in terms of the generalized James, von Neumann-Jordan, Zb?ganu constants, the Ptolemy constant and the Dom?nguez-Benavides coefficient. Our main results extend and improve some known results in the recent literature.

In this paper, we establish strong and ?-convergence theorems of modified three-step iterations for total asymptotically nonexpansive mapping which is wider than the class asymptotically nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and generalize the corresponding results of Chang et al. [Demiclosed principle and ?-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Appl. Math. Comput. 219(5) (2012) 2611-2617], Nanjaras and Panyanak [Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. Vol. 2010, Art. ID 268780], and many others.

In this paper existence and uniqueness of fixed points for a general class of contractive and nonexpansive mappings on modular metric spaces is discussed. As an application of the theoretical results, the existence of a solution of anti-periodic boundary value problems for nonlinear first order differential equations of Carath?odory?s type is considered in the framework of modular metric spaces.

In this paper we present , for sequences of sets, the concept of generalized asymptotically $\mathcal{I}$-lacunary statistical equivalent of order $\alpha$, ($0

In this paper some new inequalities of Simpson-type are established for the classes of functions whose derivatives of absolute values are convex functions via Riemann-Liouville integrals. Also, by special selections of n;we give some reduced results. © 2017, University of Nis. All rights reserved., Firat University Scientific Research Projects Management Unit British Association for Psychopharmacology, 2010 Mathematics Subject Classification. Primary 26D15 Keywords. convex functions, Simpson-Type Inequalities,Riemann-Liouville fractional integrals Received: 10 March 2016; Accepted: 29 March 2016 Communicated by Dragan S. Djordjevi? This research is supported by Ordu University Scientific Research Projects Coordinations Unit (BAP). Project Number: YKD-280 Email addresses: erhanset@yahoo.com (Erhan Set), ahmetakdemir@agri.edu.tr (Ahmet Ocak Akdemir), mozdemirr@yahoo.com (M. Emin Özdemir)

In this paper we establish a common fixed point theorem for two maps under the generalized contractive condition in a complete metric spaces.

In this paper the statement of initial value problems for fractional differential equations with noninstantaneous impulses is given. These equations are adequate models for phenomena that are characterized by impulsive actions starting at arbitrary fixed points and remaining active on finite time intervals. Strict stability properties of fractional differential equations with non-instantaneous impulses by the Lyapunov approach is studied. An appropriate definition (based on the Caputo fractional Dini derivative of a function) for the derivative of Lyapunov functions among the Caputo fractional differential equations with non-instantaneous impulses is presented. Comparison results using this definition and scalar fractional differential equations with non-instantaneous impulses are presented and sufficient conditions for strict stability and uniform strict stability are given. Examples are given to illustrate the theory.

In this paper, we study the following gradient system on a complete Riemannian manifold M, {-x?(t) = grad'(x(t)) x(0) = x0, where ? : M ? R is a C1 function with Argmin ? ? ?. We prove that the gradient flow x(t) converges to a critical point of ? if ? is pseudo-convex, or if ? is quasi-convex and M is Hadamard. As an application to minimization, we consider a discrete version of the system to approximate a minimum point of a given pseudo-convex function ?.

In this paper, we look into a new concept of accretive mappings called ??-H((.,.),(.,.))-mixed accretive mappings in Banach spaces. We extend the concept of proximal-point mappings connected with generalized m-accretive mappings to the ??-H((.,.),(.,.))-mixed accretive mappings and discuss its characteristics like single-valuable and Lipschitz continuity. Some illustration are given in support of ??-H((.,.),(.,.))-mixed accretive mappings. Since proximal point mapping is a powerful tool for solving variational inclusion. Therefore, As an application of introduced mapping, we construct an iterative algorithm to solve variational inclusions and show its convergence with acceptable assumptions.

In this paper, we consider the Cauchy problem for the 3D MHD fluid passing through the porous medium, and provide some fundamental Serrin type regularity criteria involving the velocity or its gradient, the pressure or its gradient. This extends and improves [S. Rahman, Regularity criterion for 3D MHD fluid passing through the porous medium in terms of gradient pressure, J. Comput. Appl. Math., 270 (2014), 88-99].

In this paper, we study nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with different combinations of Riemann-Liouville and Erd?lyi-Kober type fractional integral boundary conditions. By applying a variety of tools of fixed point theory, the desired existence and uniqueness results are obtained. Examples illustrating the main results are also constructed.

We consider a scalar balance law with a strict convex flux. In this paper, we study L2 stability to a shock for a scalar balance law up to a shift function, which is based on the relative entropy. This result generalizes Leger?s works [18] and provides more a simple proof than Leger?s proof.

On Page 36 of his ``lost" notebook, Ramanujan recorded four $q$-series representations of the famous Rogers-Ramanujan continued fraction. In this paper, we establish two $q$-series representations of Ramanujan's continued fraction found in his ``lost" notebook. We also establish three equivalent integral representations and modular equations for a special case of this continued fraction. Furthermore, we derive continued-fraction representations for the Ramanujan-Weber class invariants $g_n$ and $G_n$ and establish formulas connecting $g_n$ and $G_n$. We obtain relations between our continued fraction with the Ramanujan-G\"{o}llnitz-Gordon and Ramanujan's cubic continued fractions. Finally, we find some algebraic numbers and transcendental numbers associated with a certain continued fraction $A(q)$ which is related to Ramanujan's continued fraction $F(a,b,\lambda;q),$ the Ramanujan-G\"{o}llnitz-Gordon continued fraction $H(q)$ and the Dedekind eta function $\eta(s)$.

This paper is devoted to mathematician Mirko Stojakovic, member of Serbian Academy of Sciences and Arts on the occasion of 100 years since his birth, but also 30 years since his death. The life path and the main scientific contribution are depicted.

Recently, Srivastava et al. [Integral Transforms Spec. Funct. 23 (2012), 659-683] introduced the incomplete Pochhammer symbols that led to a natural generalization and decomposition of a class of hypergeometric and other related functions as well as to certain potentially useful closed-form representations of definite and improper integrals of various special functions of applied mathematics and mathematical physics. In the present paper, our aim is to establish several formulas involving integral transforms and fractional derivatives of this family of incomplete hypergeometric functions. As corollaries and consequences, many interesting results are shown to follow from our main results.

WOS:000397996300022 The present paper is concerned with a certain sequence of the nonlinear Durrmeyer operators NDn, very recently introduced by the author [22] and [23], of the form (NDn f)(x) = integral(1)(0) K-n(x,t, f (t))dt, 0 R-0(+) is continuous and concave with psi(0) = 0, psi(u) > 0 for u > 0 : This study can be considered as an extension of the related results dealing with the classical Durrmeyer operators.

In the paper, we present new semi-analytical approach for FDE?s consisting in combination of the method of steps and a technique called differential transformation method (DTM). This approach reduces the original Cauchy problem for delayed or neutral differential equation to Cauchy problem for ordinary differential equation for which DTM is convenient and efficient method. Moreover, there is no need of any symbolic calculations or initial approximation guesstimates in contrast to methods like the homotopy analysis method, the homotopy perturbation method, the variational iteration method or the Adomian decomposition method. The efficiency of the proposed method is shown on certain classes of FDE?s with multiple constant delays including FDE of neutral type. We also compare it to the current approach of using DTM and the Adomian decomposition method where Cauchy problem is not well posed.

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

In this paper, we investigate the common fixed point property for commutative nonexpansive mappings on $\tau$-compact convex sets in normed and Banach spaces, where $\tau$ is a Hausdorff topological vector space topology that is weaker than the norm topology. As a consequence of our main results, we obtain that the set of common fixed points of any commutative family of nonexpansive self-mappings of a nonempty $clm$-compact (resp. weak* compact) convex subset $C$ of $L_1(\mu)$ with a $\sigma$-finite $\mu$ (resp. the James space $J_0$) is a nonempty nonexpansive retract of $C$.

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.

In this paper, based on a lemma giving a sufficient condition for a sequence with elements from a b-metric space to be Cauchy, we obtain Caristi-Kirk type and Boyd&Wong-Browder-Matkowski-Rus type fixed point results in the framework of b-metric spaces. In addition, we extend Theorems 1, 2 and 3 from [M. Bota,V. Ilea, E. Karapinar, O. Mle?ni?e, On ?*-?-contractive multi-valued operators in b-metric spaces and applications, Applied Mathematics & Information Sciences, 9 (2015), 2611-2620].

This paper concerns the relationship between uniform boundedness and convergence of various generalized inverses. Using the stable perturbation for generalized inverse and the gap between closed linear subspaces, we prove the equivalence of the uniform boundedness and convergence for generalized inverses. Based on this, we consider the cases for the Moore-Penrose inverses and group inverses. Some new and concise expressions and convergence theorems are provided. The obtained results extend and improve known ones in operator theory and matrix theory.

In this paper, we derive a new integral identity for differentiable function. Using this new integral identity as an auxiliary result, we derive some new two point trapezoidal like inequalities for differentiable harmonic h-convex functions. These inequalities can also be viewed as Hermite-Hadamard type inequalities. We also discuss some new special cases which can be deduced from our main results.

In this paper, we establish some new inequalities of Simpson?s type based on s-convexity via fractional integrals. Our results generalize the results obtained by Sarikaya et al. [1].

In this paper, we obtain the Gronwall type inequality for generalized fractional operators unifying Riemann-Liouville and Hadamard fractional operators. We apply this inequality to the dependence of the solution of differential equations, involving generalized fractional derivatives, on both the order and the initial conditions. More properties for the generalized fractional operators are formulated and the solutions of initial value problems in certain new weighted spaces of functions are established as well.

In this paper, the problem of existence of mild solutions for a stochastic Volterra integrodifferential equation with delayed impulses and driven by a fractional Brownian motion (Hurst parameter H ? (1/2,1)) is investigated. Here, we assume that the delayed impulses are linear and impulsive transients depend on not only their current but also historical states of the system. Utilizing the fixed point theorem combine with fractional power of operators and the semi-group theory, sufficient conditions that guarantee the existence and uniqueness of mild solutions for such equation are obtained. Finally, an example is presented to demonstrate the effectiveness of the proposed results.

Deniz, Emre/0000-0003-0546-4229 WOS: 000408376500026 In this paper we construct new integral type operators including heritable properties of Baskakov Durrmeyer and Baskakov Kantorovich operators. Results concerning convergence of these operators in weighted space and the hypergeometric form of the operators are shown. Voronovskaya type estimate of the pointwise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, we give a direct approximation theorem for the operators in suitable weighted Lp space on [0; infinity).

In this paper, we consider the problem of inserting semi-continuous function above the (generalized) real-valued function in a monotone fashion. We provide some characterizations of stratifiable spaces, semi-stratifiable spaces, and $k$-monotonically countably metacompact spaces ($k$-MCM) and so on. It is established that: \begin{enumerate} \item A space $X$ is $k$-MCM if and only if for each locally bounded real-valued function $h: X\rightarrow \mathbb{R}$, there exists a lower semi-continuous and $k$-upper semi-continuous function $h': X \rightarrow \mathbb{R}$ such that (i) $ | h| \leq h' $; (ii) $h'_1 \leq h'_2$ whenever $| h_1| \leq | h_2|$. \item A space $X$ is stratifiable if and only if for each function $h: X\rightarrow \mathbb{R}^*$ ($\mathbb{R}^*$ is the generalized real number set), there is a lower semi-continuous function $h': X\rightarrow \mathbb{R}^*$ such that (i) $ h'$ is locally bounded at each $x\in U_h$ with respect to $\mathbb{R}$, where $U_h=\{x\in X: h \text{~is locally bounded at ~}x \text{~with respect to~} \mathbb{R}\}$; (ii) $|h| \leq h'$; (iii) $h'_1\leq h'_2$ whenever $| h_1|\leq | h_2|$. \end{enumerate} We give a negative answer to the problem posed by K.D. Li \cite{12}.

This paper improves and generalizes the operator versions of Kantorovich and Wielandt inequalities for positive linear maps on Hilbert space and presents more general and precise results compared to many previous results due to Fu and He [Linear Multilinear Algebra, 63(3) (2015), 571-577.] and Zhang [Banach J. Math. Anal., 9(1) (2015), 166-172.].

In this paper, using Bregman functions, we introduce a new Halpern-type iterative algorithm for finding common zeros of finitely many maximal monotone operators and obtain a strongly convergent iterative sequence to the common zeros of these operators in a reflexive Banach space. Furthermore, we study Halpern-type iterative schemes for finding common solutions of a finite system of equilibrium problems and null spaces of a -inverse strongly monotone mapping in a 2-uniformly convex Banach space. Some applications of our results to the solution of equations of Hammerstein-type are presented. Our scheme has an advantage that we do not use any projection of a point on the intersection of closed and convex sets which creates some difficulties in a practical calculation of the iterative sequence. So the simple construction of Halpern iteration provides more flexibility in defining the algorithm parameters which is important from the numerical implementation perspective. Presented results improve and generalize many known results in the current literature.

The aim of this paper is to generalize celebrated results due to Boyd and Wong [2] and Matkowski [9] and also to provide yet new solutions to the once open problem on the existence of a contractive mapping which possesses a fixed point but is not continuous at the fixed point. Besides continuous mappings our results also apply to discontinuous mappings which include threshold operations that are integral part of many a phenomena.

In this paper, firstly, we introduce the notion of R-complete metric spaces. This notion let us to consider fixed point theorem in R-complete instead of complete metric spaces. Secondly, as motivated by the recent work of Amini-Harandi (Fixed Point Theory Appl. 2012, 2012:215), we explain a new generalized contractive condition for set-valued mappings and prove a fixed point theorem in R-complete metric spaces which extends some well-known results in the literature. Finally, some examples are given to support our main theorem and also we find the existence of solution for a first-order ordinary differential equation.

The aim of the present paper is to show the significance of the concept of orbital continuity introduced by Ciric. We prove that orbital continuity of a pair of R-weak commuting self-mappings of type Af or of type A1 of a complete metric space is equivalent to fixed point property under Jungck type contraction. We also establish a situation in which orbital continuity is a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are necessarily discontinuous at the fixed point.

The aim of this paper is to prove a counterpart of the Banach fixed point principle for mappings f: l?(X)? X, where X is a metric space and l?(X) is the space of all bounded sequences of elements from X. Our result generalizes the theorem obtained by Miculescu and Mihail in 2008, who proved a counterpart of the Banach principle for mappings f:Xm ? X, where Xm is the Cartesian product of m copies of X. We also compare our result with a recent one due to Secelean, who obtained a weaker assertion under less restrictive assumptions. We illustrate our result with several examples and give an application.

In this note, we point out several gaps in the paper ?On the lower bound for a class of harmonic functions in the half space? by Zhang, Deng and Kou (Acta Math. Sci. Ser. B Engl. Ed., 32(4), 2012) and give the main results under weaker conditions.