Abstract: In this paper, we obtain some sufficient conditions for the existence and uniqueness of point of coincidence by using simulation functions in the context of metric spaces and prove some interesting results. Our results generalize the corresponding results of [5, 8, 13, 14, 16] in several directions. Also, we provide an example which shows that our main result is a proper generalization of the result of Jungck [American Math. Monthly 83(1976) 261-263], L-de-Hierro et al. [J. Comput. Appl. Math 275(2015) 345-355] and of Olgun et al. [Turk. J. Math. (2016) 40:832-837].

Abstract: The objective of this paper is to extend Ulam-Hyers stability and Ulam-Hyers-Rassias stability theory to differential equations with delay and in the frame of a certain class of a generalized Caputo fractional derivative with dependence on a kernel function. We discuss the conditions such delay generalized Caputo fractional differential equations should satisfy to be stable in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. To demonstrate our results two examples are presented.

Abstract: The new definition of the fractional derivative was defined by Atangana and Baleanu in 2016. They used the generalized Mittag-Leffer function with the non-singular and non-local kernel. Further, their version provides all properties of fractional derivatives. Our aim is to analyse the Keller-Segel model with Caputo and Atangana-Baleanu fractional derivative in Caputo sense. Using fixed point theory, we first show the existence of coupled solutions. We then examine the uniqueness of these solutions. Finally, we compare our results numerically by modifying our model according to both definitions, andwedemonstrate these results on the graphs in detail. All computations were done using Mathematica.

Abstract: Conformable fractional derivative is introduced by the authors Khalil et al. In this study we develop their concept and introduce multi-variable conformable derivative for a vector valued function with several variables

Abstract: Statistical (C,1) summability and a Korovkin type approximation theorem has been proved by Mohiuddine et al. [20] (see [S. A. Mohiuddine, A. Alotaibi and M. Mursaleen, Statistical summability (C,1) and a Korovkin type approximation theorem, J. Inequal. Appl. 2012 (2012), Article ID 172, 1-8). In this paper, we apply statistical deferred Cesaro summability method to prove a Korovkin type approximation theorem for the set of functions 1, e-x and e-2x defined on a Banach space C[0;1) and demonstrate that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. We also establish a result for the rate of statistical deferred Cesaro summability method. Some interesting examples are also discussed here in support of our definitions and results.

Abstract: In this paper, we give expressions for the generalized Drazin inverse of a (2,2,0) block matrix over a Banach algebra under certain circumstances, utilizing which we derive the generalized Drazin inverse of a 2× 2 block matrix in a Banach algebra under weaker restrictions. Our results generalize and unify several results in the literature.

Abstract: This short note concerns with two inequalities in the geometry of gradient Ricci solitons $(g, f, \lambda )$ on a smooth manifold $M$. These inequalities provide some relationships between the curvature of the Riemannian metric $g$ and the behavior of the scalar field $f$ through two second order equations satisfied by the scalar $\lambda $. We propose several generalizations of Ricci solitons to the setting of manifolds endowed with linear connections, not necessary of metric type.

Abstract: In the present investigation, we consider two new general subclasses HΣm(τ, γ;α) and HΣm(τ, γ;β) of Σm consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. For functions belonging to the two classes introduced here, we derive estimates on the initial coefficients |am+1| and |a2m+1|. Several related classes are also considered and connections to earlier known results are made. 2010 Mathematics Subject Classification: 30C45, 30C50, 30C80.

Abstract: It was shown in [15, 16] that there does not exist any warped product submanifold of a Kaehler manifold such that the spherical manifold of the warped product is proper slant. In this paper, we introduce the notion of warped product submanifolds with a slant function. We show that there exists a class of nontrivial warped product submanifolds of a Kaehler manifold such that the spherical manifold is pointwise slant by giving an example and a characterization theorem. We also prove that if the warped product is mixed totally geodesic then the warping function is constant.

Abstract: By using contemporary theory of inequalities, this study is devoted topropose a number of refinements inequalities for the Hermite$-$Hadamard'stype inequality and conclude explicit bounds for the trapezoid inequalitiesin terms of $s$-convex mappings, at most second derivative through theinstrument of generalized fractional integral operator and a considerableamount of results for special means The results of this study which are thegeneralization of those given in earlier works are obtained for functions $f$where $|f^{\prime }|$ and $|f^{\prime \prime }|$ (or $|f^{\prime }|^{q}$ and $|f^{\prime \prime }|^{q}$ for $q\geq 1$) are $s$-convex hold by applyingthe Holder inequality and the power mean inequality

Abstract: In this paper we introduce contraction mappings of Meir-Keeler types on modular metric spaces and investigate the existence and uniqueness of their fixed points. We give an example which demonstrates our theoretical results.

Abstract: In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the Hölder integral inequality and the notion of geometrically-arithmetically convexity, some new Fejér type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

Abstract: Recently, B.-Y. Chen and O.J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. In this paper, first we study pointwise slant and pointwise pseudo-slant submanifolds of almost contact metric manifolds and then using this notion, we show that there exist a non-trivial class of warped product pointwise pseudo-slant submanifolds of Sasakian manifolds by giving some useful results, including a characterization.

Abstract: We investigate a new type boundary value problem consisting of a differential-operator equation, eigendependent boundary conditions, and two supplementary conditions so-called interface conditions We give a characterisation of some spectral properties of the considered problem Particularly, it is established such properties as isomorphism and coerciveness, discreteness of the spectrum and found asymptotic formulas for eigenvalues

Abstract: Here, a fourth order singular elliptic problem involving p-biharmonic operator with Dirichlet boundary condition is established where the exponent in the singular term is different from that in the p-biharmonic operator. The existence of infinitely many solutions is proved by the variational methods in Sobolev spaces and the critical points principle of Ricceri. Finally, an example is presented.

Abstract: According to the decision information of multi-attribute decision-making problem with fuzzy and temporal characteristics, a dynamic intuitionistic fuzzy decision making method based on time preference and VIKOR is proposed. First, we determined the attribute weights under different time sequence based on intuitionistic fuzzy entropy minimization; secondly, we introduced the time degree function reflecting the decision makers’ subjective time preference, and established a multi-objective programming model to obtain time weights; then we used dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator to integrate different time periods of the intuitionistic fuzzy decision matrices; the VIKOR method is used in ranking solutions that takes account of group effectiveness maximization and individual regret minimization, and obtained the optimal scheme that is closet to ideal solution; finally, the feasibility and effectiveness of the proposed method is verified by the example of a technology innovation alliance partner selection.

Abstract: We investigate a discontinuous boundary value problem which consists of a Sturm-Liouville equation with piecewise continuous potential together with eigenparameter dependent boundary conditions and supplementary transmission conditions. We establish some spectral properties of the considered problem. In particular, it is shown that the problem under consideration has precisely denumerable many eigenvalues λ1, λ2,..., which are real and tends to +∞. Moreover, it is proven that the generalized eigenvectors form a Riesz basis of the adequate Hilbert space.

Abstract: In this article we have investigated some properties of the Nörlund and Riesz mean of sequences of complex uncertain variables. Also, we prove results on oscillating sequences of complex uncertain variables.

Abstract: Let U be a unital ?-algebra and δ : U → U be a linear map behaving like a derivation or an anti-derivation at the following orthogonality conditions on elements of U: xy = 0, xy? = 0, xy = yx = 0 and xy? = y?x = 0. We characterize the map δ when U is a zero product determined algebra. Special characterizations are obtained when our results are applied to properly infinite W?-algebras and unital simple C?-algebras with a non-trivial idempotent.

Abstract: In this paper, we present a unified approach to the study of shift-invariant systems to be frames on local fields of positive characteristic. We establish a necessary condition and three sufficient conditions under which the shift-invariant systems on local fields constitute frames for L2(K). As an application of these results, we obtain some known conclusions about the Gabor frames and wavelet frames on local fields.

Abstract: The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based on (p,q)-integers. We prove uniform approximation by means of Bohman-Korovkin type theorem, rate of convergence using total modulus of smoothness and degree of approximation via second order modulus of smoothness, Peetre’s K-functional, Lipschitz type class.

Abstract: We consider gradient Ricci solitons on multiply warped product manifolds. We find the necessary and sufficient conditions for multiply warped product manifolds to be gradient Ricci solitons.

Abstract: We study the split feasibility problem (SFP) involving the fixed point problems (FPP) in the framework of p-uniformly convex and uniformly smooth Banach spaces. We propose a Halpern-type iterative scheme for solving the solution of SFP and FPP of Bregman relatively nonexpansive semigroup. Then we prove its strong convergence theorem of the sequences generated by our iterative scheme under implemented conditions. We finally provide some numerical examples and demonstrate the efficiency of the proposed algorithm. The obtained result of this paper complements many recent results in this direction.

Abstract: In the present paper, first we prove some results by using fundamental properties of totally real statistical submanifolds immersed into holomorphic statistical manifolds. Further, we obtain the generalized Wintgen inequality for Lagrangian statistical submanifolds of holomorphic statistical manifolds with constant holomorphic sectional curvature c. The paper finishes with some geometric consequences of obtained results.

Abstract: In this paper, we firstly introduce bijective soft matrix theory and research its operations, properties and algebraic structures in detail. Also, we present a bijective soft decision system based on the bijective soft matrix theory. Moreover, we construct a multi-bijective linguistic soft decision system by employing the matrices corresponding to the bijective soft sets generated from the linguistic variable parameters. Finally, the system’s decision algorithm and its application for a decision making problem are given. By using the algorithm, we determine both the linguistic variables according to the parameters and the parameters affecting the optimal choice according to the highest linguistic decision value.

Abstract: In this work, we want to use the Non-polynomial spline basis and Quasi-linearization method to solve the nonlinear Volterra integral equation. When the iterations of the Quasilinear technique employed in nonlinear integral equation we obtain a linear integral equation then by using the Non-polynomial spline functions and collocation method the solution of the integral equation can be approximated. Analysis of convergence is investigated. At the end, some numerical examples are presented to show the effectiveness of the method.

Abstract: In this paper, we first improve the boundary Schwarz lemma for holomorphic self-mappings of the unit ball Bn, and then we establish the boundary Schwarz lemma for harmonic self-mappings of the unit diskD and pluriharmonic self-mappings of Bn. The results are sharp and coincides with the classical boundary Schwarz lemma when n = 1.

Abstract: In this paper we show many spectral properties that are inherited by m-complex symmetric and m-skew complex symmetric operators and give new results or recapture some known ones for complex symmetric operators.