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In this paper, we present some fixed point results satisfying generalized contractive condition with new auxiliary function in complete metric spaces. More precisely, the structure of the paper is the following. In the first section, we present some useful notions and results. The main aim of second section is to establish some new fixed point results in complete metric spaces. Finally, in the third section, we show the validity and superiority of our main results by suitable example. Also, as an application of our main result, some interesting corollaries have been included, which make our concepts and results effective. Our main result generalizes some well known existing results in the literature.

In this paper, we introduce and investigate an interesting subclass of meromorphic bi-univalent functions defined on Δ = {z ∈ ℂ: 1 < |z| < ∞}. For functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper generalize and improve some recent works.

In the present paper we introduce the sequence spaces c0{ℳ, Λ , p, q}, c{ℳ, Λ, p, q} and l ∞ {ℳ, Λ, p, q} defined by a Musielak-Orlicz function ℳ = (ℳk). We study some topological properties and prove some inclusion relations between these spaces.

In this paper our main interest is to introduce a new type of generalized open sets defined in terms of an operation on a generalized topological space. We have studied some properties of this newly defined sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have studied some preservation theorems in terms of some irresolute functions.

The bucket recursive tree is a natural multivariate structure. In this paper, we apply a trivariate generating function approach for studying of the depth and distance quantities in this tree model with variable bucket capacities and give a closed formula for the probability distribution, the expectation and the variance. We show as j → ∞, lim-iting distributions are Gaussian. The results are obtained by presenting partial differential equations for moment generating functions and solving them.

In this paper we define dual-complex numbers with generalized Jacobsthal coefficients. We introduce one-parameter generalization of dual-complex Jacobsthal numbers - dual-complex r-Jacobsthal numbers. We investigate some algebraic properties of introduced numbers, among others Binet type formula, Catalan, Cassini, d’Ocagne and Honsberger type identities. Moreover, we present the generating function, summation formula and matrix generator for these numbers. The results are generalization of the properties for the dual-complex Jacobsthal numbers.

An induced star-triangle factor of a graph G is a spanning subgraph F of G such that each component of F is an induced subgraph on the vertex set of that component and each component of F is a star (here star means either K1,n, n ≥ 2 or K2) or a triangle (cycle of length 3) in G. In this paper, we establish that every graph without isolated vertices admits an induced star-triangle factor in which any two leaves from different stars K1,n (n ≥ 2) are non-adjacent.

In this paper, we introduce the notion of Walsh shift-invariant space and present a unified approach to the study of shift-invariant systems to be frames in L2(ℝ+). We obtain a necessary condition and three sufficient conditions under which the Walsh shift-invariant systems constitute frames for L2(ℝ+). Furthermore, we discuss applications of our main results to obtain some known conclusions about the Gabor frames and wavelet frames on positive half line.

In this paper we consider two subclasses of bi-univalent functions defined by the Horadam polynomials. Further, we obtain coefficient estimates for the defined classes.

In this paper we introduce the new types of separation axioms called λD − R0 and λD − R1 spaces, by using λD-open set. The notion λD − R0 and λD − R1 spaces are introduced and some of their properties are investigated.

In this paper we introduce and study the split Horadam quaternions. We give some identities, among others Binet’s formula, Catalan’s, Cassini’s and d’Ocagne’s identities for these numbers.

In this paper the conditions and the findings of a simulation study is presented for assessing the effect size of users’ consciousness to the computer network vulnerability in risky cyber attack situations at a certain business. First a simple model is set up to classify the groups of users according to their skills and awareness then probabilities are assigned to each class describing the likelihood of committing dangerous reactions in case of a cyber attack. To quantify the level of network vulnerability a metric developed in a former work is used. This metric shows the approximate probability of an infection at a given business with well specified parameters according to its location, the type of the attack, the protections used at the business etc. The findings mirror back the expected tendencies namely if the number of conscious user is on the

Barnette’s conjecture states that every three connected cubic bipartite planar graph (CPB3C) is Hamiltonian. In this paper we show the existence of a family of CPB3C Hamiltonian graphs in which large and large subgraphs are non-Hamiltonian.

In the paper, the author discusses and computes bounds of the sine and cosine along straight lines on the complex plane.

In this paper, we study the Γ-hyperrings via T-fuzzy hyperideals. By means of the use of a triangular norm T, we define, characterize and study the T-fuzzy left and right hyperideals, T-fuzzy quasi-hyperideal and bi-hyperideal in Γ-hyperrings and some related properties are investigated. Regular Γ-hyperrings are characterized in terms of T-fuzzy quasi-hyperideal and T-fuzzy bi-hyperideal. We also introduce the T-(λ, µ)-fuzzy bi-hyperideals in Γ-hyperrings and investigate some of their properties.

Let (pn) and (qn) be any two non-negative real sequences with R n : = ∑ k = 0 n p k q n - k ≠ 0 ( n ∈ 𝕅 ) {{\rm{R}}_{\rm{n}}}: = \sum\limits_{{\rm{k}} = 0}^{\rm{n}} {{{\rm{p}}_{\rm{k}}}{{\rm{q}}_{{\rm{n}} - {\rm{k}}}}} \ne 0\,\,\,\,\left( {{\rm{n}} \in {\rm\mathbb{N}}} \right) With E n 1 {\rm{E}}_{\rm{n}}^1 − we will denote the Euler summability method. Let (xn) be a sequence of real or complex numbers and set N p , q n E n 1 : = 1 R n ∑ k = 0 n p k q n - k 1 2 k ∑ v = 0 k ( v k ) x v {\rm{N}}_{{\rm{p}},{\rm{q}}}^{\rm{n}}{\rm{E}}_{\rm{n}}^1: = {1 \over {{{\rm{R}}_{\rm{n}}}}}\sum\limits_{{\rm{k}} = 0}^{\rm{n}} {{{\rm{p}}_{\rm{k}}}{{\rm{q}}_{{\rm{n - k}}}}{1 \over {{2^{\rm{k}}}}}\sum\limits_{{\rm{v}} = 0}^{\rm{k}} {\left( {_{\rm{v}}^{\rm{k}}} \right){{\rm{x}}_{\rm{v}}}} } for n ∈ ℕ. In this paper, we present necessary and sufficient conditions under which the existence of the st− limit of (xn) follows from that of st - N p , q n E n 1 {\rm{st - N}}_{{\rm{p}},q}^{\rm{n}}{\rm{E}}_{\rm{n}}^1 − limit of (xn). These conditions are one-sided or two-sided if (xn) is a sequence of real or complex numbers, respectively.

Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study the concept of gr-n-ideals of R. We obtain many results concerning gr-n-ideals. Some characterizations of gr-n-ideals and their homogeneous components are given.

An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective. An IASI $f$ is said to be a weak IASI if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. A graph which admits a weak IASI may be called a weak IASI graph. The set-indexing number of an element of a graph $G$, a vertex or an edge, is the cardinality of its set-labels. The sparing number of a graph $G$ is the minimum number of edges with singleton set-labels, required for a graph $G$ to admit a weak IASI. In this paper, we study the admissibility of weak IASI by certain graph powers and their sparing numbers., 14 pages, 6 figures, submitted

In this paper, we propose a new approximate method, namely fractional natural decomposition method (FNDM) in order to solve a certain class of nonlinear time-fractional wave-like equations with variable coefficients. The fractional natural decomposition method is a combined form of the natural transform method and the Adomian decomposition method. The nonlinear term can easily be handled with the help of Adomian polynomials which is considered to be a clear advantage of this technique over the decomposition method. Some examples are given to illustrate the applicability and the easiness of this approach.

For a commutative ring R with 1 ≠ 0, a compressed zero-divisor graph of a ring R is the undirected graph ΓE(R) with vertex set Z(RE) \ {[0]} = RE \ {[0], [1]} defined by RE = {[x] : x ∈ R}, where [x] = {y ∈ R : ann(x) = ann(y)} and the two distinct vertices [x] and [y] of Z(RE) are adjacent if and only if [x][y] = [xy] = [0], that is, if and only if xy = 0. In this paper, we study the metric dimension of the compressed zero divisor graph ΓE(R), the relationship of metric dimension between ΓE(R) and Γ(R), classify the rings with same or different metric dimension and obtain the bounds for the metric dimension of ΓE(R). We provide a formula for the number of vertices of the family of graphs given by ΓE(R×𝔽). Further, we discuss the relationship between metric dimension, girth and diameter of ΓE(R).

Contractions represents the foundation stone of nonlinear analysis. That is the reason why we propose to unify two different type of contractions: almost contractions, introduced by V. Berinde in [2] and local contractions (Martins da Rocha and Filipe Vailakis in [7]). These two types of contractions operate in different space settings: in metric spaces (almost contractions) and semimetric spaces (for local contractions). That new type of contraction was built up in a new space setting, which is the pseudometric space. The main results of this paper represent the extension for various type of operators on pseudometric spaces, such as: generalized ALC, Ćirić-typeALC, quasi ALC, Ćirić-Reich-Rustype ALC. We propose to study the existence and uniqueness of their fixed points, and also the continuity in their fixed points, with a large number of examples for ALC-s.

Let R be a ring, MR a module, S a monoid, ω : S → End(R) a monoid homomorphism and R * S a skew monoid ring. Then M[S] = {m1g1 + · · · + mngn | n ≥ 1, mi ∈ M and gi ∈ S for each 1 ≤ i ≤ n} is a module over R ∗ S. A module MR is Baer (resp. quasi-Baer) if the annihilator of every subset (resp. submodule) of M is generated by an idempotent of R. In this paper we impose S-compatibility assumption on the module MR and prove: (1) MR is quasi-Baer if and only if M[s]R∗S is quasi-Baer, (2) MR is Baer (resp. p.p) if and only if M[S]R∗S is Baer (resp. p.p), where MR is S-skew Armendariz, (3) MR satisfies the ascending chain condition on annihilator of submodules if and only if so does M[S]R∗S, where MR is S-skew quasi-Armendariz.

The connection between polylogarithmic functions and Euler sums is well known. In this paper we explore the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider mainly, polylogarithmic functions with negative arguments, thereby producing new results and extending the work of Freitas. Many examples of integrals of products of polylogarithmic functions in terms of Riemann zeta values and Dirichlet values will be given.

This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.

The object of the present paper is to study of two certain subclass of analytic functions related with Booth lemniscate which we denote by $\mathcal{BS}(\alpha)$ and $\mathcal{BK}(\alpha)$. Some properties of these subclasses are considered., Comment: 9 pages

In this paper, the concept of fractional q-calculus and generalized Al-Oboudi differential operator defining certain classes of analytic functions in the open disc are used. The results investigated for these classes of functions include the coefficient estimates, inclusion relations, extreme points and some more properties.

In the paper, the authors find the sum of the Lah numbers and make sure that the Kummer confluent hypergeometric function 1F1(n+ 1; 2; z) has only n− 1real and negative zeros.

The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.

The main object of the present paper is to introduce and study the generalized Laguerre matrix polynomials for a matrix that satisfies an appropriate spectral property. We prove that these matrix polynomials are characterized by the generalized hypergeometric matrix function. An explicit representation, integral expression and some recurrence relations in particular the three terms recurrence relation are obtained here. Moreover, these matrix polynomials appear as solution of a differential equation.

In this paper, we consider the tangent bundle of a Riemannian manifold (M, g) with g-natural metrics and among all of these metrics, we specify those with respect to which the unit tangent sphere bundle with induced g-natural metric is totally geodesic. Also, we equip the unit tangent sphere bundle T1M with g-natural contact (paracontact) metric structures, and we show that such structures are totally geodesic K-contact (K-paracontact) submanifolds of TM, if and only if the base manifold (M, g) has positive (negative) constant sectional curvature. Moreover, we establish a condition for g-natural almost contact B-metric structures on T1Msuch that these structures be totally geodesic submanifolds of TM.

In this paper, we discuss the problem of meromorphic functions sharing small function and present one theorem which extend a result of K. S. Charak and Banarasi Lal [16].

In this paper we analyze the monotony of the function ln Γ ( x ) ln ( x 2 + τ ) - ln ( x + τ ) ${{{\rm{ln}}\,\Gamma ({\rm{x}})} \over {{\rm{ln}}\,({\rm{x}}^2 + \tau) - {\rm{ln}}\,({\rm{x}} + \tau)}}$ , for τ > 0. Such functions have been used from different authors to obtain inequalities concerning the gamma function.

In this paper, we introduce the concepts of rational type and subrational type contractive mappings. We expand and improve some fixed point theorems obtained by Alsulami et al. (Fixed Point Theory Appl., 2015, 2015: 97). Moreover, we give an example to support our results.

Erdal Ekici has introduced and studied nearly continuous multifunctions in [5]. The purpose of the present paper is to introduce and study upper and lower nearly ω-continuous multifunctions as a weaker form of upper and lower nearly continuous multifunctions. Basic characterizations, several properties of upper and lower nearly ω-continuous multifunctions are investigated.

In this paper, will show that a symmetric group of prime degree p ≥ 5 is recognizable by its order and a special conjugacy class size of (p − 1)!.

Unbounded solutions for the iterative-difference equation f 2 ( x ) = λ f ( x + a ) + μ x , x ∈ ℝ , \font\msbm=MSBM10$${\rm{f}}^2 ({\rm{x}}) = \lambda {\rm{f}}({\rm{x}} + {\rm{a}}) + \mu {\rm{x}},\;\;\;{\rm{x}} \in {\msbm R},$$ have been considered in [Continuous solutions of an iterative-difference equation and Brillouët problem, Publ. Math. Debrecen, 78 (2011), 613–624], where λ, μ, a are real constants. In this paper, we continue to study the solutions not being included there, and further give the convex and concave ones. Finally, continuous solutions of this equation with an extra item were also given, which continuously depend on the parameter a.

In this paper we prove the existence of the unique fixed point for the pair of weakly compatible self-mappings satisfying some Ф-type contractive conditions in the framework of S-metric spaces. Our results generalize, extend, unify, complement and enrich recently fixed point results in existing literature.

In this paper we define a bridge between pairings and colorings of the hypergraphs by introducing a generalization of pairs called t-cakes for t ∈ ℕ, t ≥ 2. For t = 2 the 2-cakes are the same as the well-known pairs of system of distinct representatives, that can be turned to pairing strategies in Maker-Breaker hypergraph games, see Hales and Jewett [12]. The two-colorings are the other extremity of t-cakes, in which the whole ground set of the hypergraph is one big cake that we divide into two parts (color classes). Starting from the pairings (2-cake placement) and two-colorings we define the generalized t-cake placements where we pair p elements by q elements (p, q ∈ ℕ, 1 ≤ p, q < t, p + q = t). The method also gives bounds on the condition of winnings in certain biased Chooser-Picker games, which can be introduced similarly to Beck [3]. We illustrate these ideas on the k-in-a-row games for different values of k on the infinite chessboard.

The purpose of this paper is to study Ricci solitons on QR-hypersurfaces M of a quaternionic space form ℚn such that the shape operator A with respect to N has one eigenvalue. We prove that Ricci soliton on QR-hypersurfaces M with eigenvalue zero is steady and for eigenvalue nonzero is shrinking.

In this paper we establish some vector inequalities for two operators related to Schwarz and Buzano results. We show amongst others that in a Hilbert space H we have the inequality 1 2 [ 〈 | A | 2 + | B | 2 2 x , x 〉 1 / 2 〈 | A | 2 + | B | 2 2 y , y 〉 1 / 2 + | 〈 | A | 2 + | B | 2 2 x , y 〉 | ] ≥ | 〈 Re ( B * A ) x , y 〉 | $${1 \over 2}\left[ {\left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over 2}{\rm{x}},{\rm{x}}} \right\rangle ^{1/2} \left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over 2}{\rm{y}},{\rm{y}}} \right\rangle ^{1/2} + \left| {\left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over {\rm{2}}}} {\rm{x}},{\rm{y}}\right\rangle } \right|} \right] \ge \left| {\left\langle {{\mathop{\rm Re}\nolimits} ({\rm{B}}*{\rm{A}})\,{\rm{x}},{\rm{y}}} \right\rangle } \right|$$ for A, B two bounded linear operators on H such that Re (B*A) is a nonnegative operator and any vectors x, y ∈ H. Applications for norm and numerical radius inequalities are given as well.

In this paper, with use of Lyapunov functional, we investigate asymptotic stability of solutions of some nonlinear differential equations of third order with delay. Our results include and improve some well-known results in the literature.

In the paper are studied the properties of the image of a class of analytic functions defined by the Ruscheweyh derivative trough the Bernardi operator.

WOS: 000420586300001, In this paper our aim is to find the solutions of time and space fractional heat differential equations by using new definition of fractional derivative called conformable fractional derivative. Also based on conformable fractional derivative definition conformable Fourier Transform is defined. Fourier sine and Fourier cosine transform definitions are given and space fractional heat equation is solved by conformable Fourier transform.

Bayram, Bengü (Balikesir Author), The focal representation of a generic regular curve gamma in Em+1 consists of the centers of the osculating hyperplanes. A k-slant helix gamma in Em+1 is a (generic) regular curve whose unit normal vector V-k makes a constant angle with a fixed direction (U) over right arrow in Em+1. In the present paper we proved that if gamma is a k-slant helix in Em+1, then the focal representation C-gamma of gamma in Em+1 is an (m - k + 2)-slant helix in Em+1.

In this paper, we study three-step iteration process for Ciric-quasi contractive operator and establish strong convergence theorems for above mentioned operator and schemes in the setting of CAT(0) spaces. Our result extends and generalizes some previous work from the existing literature (see, e.g., [4, 30] and some others).

A generalized hypersubstitution of type τ is a mapping which maps any operation symbol to the set of all terms of the same type which does not necessarily preserve the arity. The set of all generalized hypersubstitutions together with a binary operation and the identity element forms a monoid. In this paper we determine all maximal idempotent submonoids of this monoid of type τ = (n).

In the present investigation, we find estimates on the coefficients |a2| and |a3| for functions in the function class SΣ (λ,φ) . The results presented in this paper improve or generalize the recent work of Magesh and Yamini

The Nelder-Mead simplex method is a widespread applied numerical optimization method with a vast number of practical applications, but very few mathematically proven convergence properties. The original formulation of the algorithm is stated in Rn using terms of Euclidean geometry. In this paper we introduce the idea of a hyperbolic variant of this algorithm using the Poincaré disk model of the Bolyai- Lobachevsky geometry. We present a few basic properties of this method and we also give a Matlab implementation in 2 and 3 dimensions

In this paper we study the continuous dependence and the differentiability with respect to the parameter λ ∈ [λ1, λ2] of the solution operator S : [λ1, λ2] → L2[a, b] for a mixed Fredholm-Volterra type integral equation. The main tool is the fiber Picard operators theorem (see [9], [8], [11], [3] and [2]).

A result concerning the starlikeness of the image of the Alexander operator is improved in this paper. The techniques of differential subordinations are used.