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International Conference on Approximation and Computation - Theory and Applications (ACTA) -- NOV 30-DEC 02, 2017 -- Belgrade, SERBIA KUCUKOGLU, IREM/0000-0001-9100-2252 WOS: 000463447500004 The first aim of this paper is to give identities and relations for a new family of the combinatorial numbers and the Apostol-Euler type numbers of the second kind, the Stirling numbers, the Apostol-Bernoulli type numbers, the Bell numbers and the numbers of the Lyndon words by using some techniques including generating functions, functional equations and inversion formulas. The second aim is to derive some derivative formulas and combinatorial sums by applying derivative operators including the Caputo fractional derivative operators. Moreover, we give a recurrence relation for the Apostol-Euler type numbers of the second kind. By using this recurrence relation, we construct a computation algorithm for these numbers. In addition, we derive some novel formulas including the Stirling numbers and other special numbers. Finally, we also some remarks, comments and observations related to our results. Serbian Acad Sci & Arts, Math Inst, Univ Belgrade, Fac Mech Engn, Univ Belgrade, Fac Math, Univ Belgrade, Sch Elect Engn, Univ Nis, Univ Kragujevac, Fac Sci, Univ Novi Sad, Fac Sci Scientific Research Project Administration of Akdeniz UniversityAkdeniz University [FBA-2018-3292] The present paper was supported by Scientific Research Project Administration of Akdeniz University (with Project Number: FBA-2018-3292).

The paper studies the open-hereditary property of semi-separation axioms and applies it to the study of digital topological spaces such as an n-dimensional Khalimsky topological space, a Marcus-Wyse topological space and so on. More precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms such as T1/2 , semi-T1/2 , semi-T1, semi-T2, etc. Besides, using the finite or the infinite product property of the semi-Ti-separation axiom, i ? {1,2}, we prove that the n-dimensional Khalimsky topological space is a semi-T2-space. After showing that not every subspace of the digital topological spaces satisfies the semi-Ti-separation axiom, i ?{1,2}, we prove that the semi-Tiseparation property is open-hereditary, i ? {1,2}. All spaces in the paper are assumed to be nonempty and connected.

The aim of the article is to establish the structure of partial cone b-metric spaces over Banach algebras. Topological and structural properties are investigated of the new spaces. We also define generalized Lipschitz mappings and give their application in fixed point theory. The results presented in this paper substantially extend and strengthen the results of the literature. Few examples are provided to support our conclusions and as an application we establish the existence and uniqueness of a solution to a class of system of nonlinear integral equations.

© 2019, University of Nis. All rights reserved. In this paper we introduced the concept of strong probabilistic metric spaces (sPM spaces) and we show some of its basic properties. In this frame we present several fixed point results for mappings of contractive type. Our results generalize and unify several fixed point theorems in literature. Finally, we give some possible applications of our results.

In this paper, we define an involute and an evolving involute of order k of a null Cartan curve in Minkowski space En1 for n ? 3 and 1 ? k ? n-1. In relation to that, we prove that if a null Cartan helix has a null Cartan involute of order 1 or 2, then it is Bertrand null Cartan curve and its involute is its Bertrand mate curve. In particular, we show that Bertrand mate curve of Bertrand null Cartan curve can also be a non-null curve and find the relationship between the Cartan frame of a null Cartan curve and the Frenet or the Cartan frame of its non-null or null Cartan involute of order 1 ? k ? 2. We show that among all null Cartan curves in E31 , only the null Cartan cubic has two families of involutes of order 1, one of which lies on B-scroll. We also give some relations between involutes of orders 1 and 2 of a null Cartan curve in Minkowski 3-space. As an application, we show that involutes of order 1 of a null Cartan curve in E31 , evolving according to null Betchov-Da Rios vortex filament equation, generate timelike Hasimoto surfaces.

In this paper, we present a unique polar-like decomposition theorem for rectangular complex matrices. Applying this decomposition, we define on the set of rectangular matrices a new partial ordering called WL(weak L?wner) partial order ? an extension of the GL(generalized L?wner) partial order, and derive some basic properties of the new partial ordering.

Very recently, Shahzad et al. [RACSAM 111 (2017) 307-324] introduced the notion of (A,S)- contractions which unifies several well known nonlinear type contractions (e.g. R-contractions, Z-contractions, L-contractions etc.) in one go. In this paper, we introduce the notion of generalized (A,S)f-contractions and utilize the same to present some coincidence and common fixed point results for a pair of self-mappings (g,f)defined on a metric space endowed with a binary relation S. In this course, we ought to introduce some new notions namely: (I,S)-continuity, (I,S)-compatibility and local (g,f)-transitivity. Consequently, several results involving R-contractions and Z-contractions are deduced. Finally, we furnish illustrative examples to demonstrate the utility of our results.

In this paper, categorical properties of L-fuzzifying convergence spaces are investigated. It is shown that (1) the category L-FYC of L-fuzzifying convergence spaces is a strong topological universe; (2) the category L-FYKC of L-fuzzifying Kent convergence spaces, as a bireflective and bicoreflective subcategory of L-FYC, is also a strong topological universe; (3) the category L-FYLC of L-fuzzifying limit spaces, as a bireflective subcategory of L-FYKC, is a topological universe.

In this paper, weobtained best proximity coincidence point theorems for ?-Geraghty contractions in the setting of complete metric spaces by using weak P-property. Also we presented some examples to prove the validity of our results. Our results extended and unify many existing results in the literature. Moreover, in the last section as applications of our main results, we can apply some coincidence best proximity point and coupled coincidence proximity point on metric spaces endowed with an arbitrary binary relation.

In this paper, we study the differential geometry of contact CR-submanifolds of a cosymplectic manifold. Necessary and sufficient conditions are given for a submanifold to be a contact CR-submanifold in cosymplectic manifolds and cosymplectic space forms. Finally, the induced structures on submanifolds are investigated, these structures are categorized and we discuss these results.

In this paper we study the uniform approximation of functions by Favard-Sz?sz-Mirakyan operators of max-product type in some exponential weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity.

This paper introduces the definition of a Lie rough group as a natural development of the concepts of a smooth manifold and a rough group on an approximation space. Furthermore, the properties of Lie rough groups are discussed. It is shown that every Lie rough group is a topological rough group, and that the product of two Lie rough groups is again a Lie rough group. We define the concepts of Lie rough subgroups and Lie rough normal subgroups. Finally, our aim is to give an example by using definition of Lie rough homomorphism sets G and H.

Tauberian theorem provides a criterion for the convergence of non convergent (summable) sequences. In this paper, we established a Tauberian theorem for nth real sequences via Ces?ro summability by using de la Vall?e Poussin mean and slow oscillation. The discussion and findings are capable to unify several useful concepts in the literature, and should also provide nontrivial extension of several results. Some examples are incorporated in support of our definitions and results. The findings are further expected to be helpful in designing and study several other interesting problems in summability theory and applications.

The main aim of the present paper is to define new soft separation axioms which lead us, first, to generalize existing comparable properties via general topology, second, to eliminate restrictions on the shape of soft open sets on soft regular spaces which given in [22], and third, to obtain a relationship between soft Hausdorff and new soft regular spaces similar to those exists via general topology. To this end, we define partial belong and total non belong relations, and investigate many properties related to these two relations. We then introduce new soft separation axioms, namely p-soft Ti-spaces (i = 0,1,2,3,4), depending on a total non belong relation, and study their features in detail. With the help of examples, we illustrate the relationships among these soft separation axioms and point out that p-soft Ti-spaces are stronger than soft Ti-spaces, for i = 0,1,4. Also, we define a p-soft regular space, which is weaker than a soft regular space and verify that a p-soft regular condition is sufficient for the equivalent among p-soft Ti-spaces, for i = 0,1,2. Furthermore, we prove the equivalent among finite p-soft Ti-spaces, for i = 1,2,3 and derive that a finite product of p-soft Ti-spaces is p-soft Ti, for i = 0,1,2,3,4. In the last section, we show the relationships which associate some p-soft Ti-spaces with soft compactness, and in particular, we conclude under what conditions a soft subset of a p-soft T2-space is soft compact and prove that every soft compact p-soft T2-space is soft T3-space. Finally, we illuminate that some findings obtained in general topology are not true concerning soft topological spaces which among of them a finite soft topological space need not be soft compact.

In this paper, we study the existence and uniqueness of best proximity points for cyclic Meir-Keeler contraction mappings in metric spaces with the property W-WUC. Also, the existence of best proximity points for set-valued cyclic Meir-Keeler contraction mappings in metric spaces with the property WUC are obtained

WOS: 000423281300008, In this paper, alpha-Meir-Keeler and generalized alpha-Meir-Keeler contractions on Branciari b-metric spaces are introduced. Existence and uniqueness of fixed points of such contractions are discussed and related theorems are proved. Various consequences of the main results are also presented.

In view of the relationship with the Kr\"{a}tzel function, we derive a new series representation for the $\lambda$-generalized Hurwitz-Lerch Zeta function introduced by H.M. Srivastava [Appl. Math. Inf. Sci. 8 (2014) 1485--1500] and determine the monotonicity of its coefficients. An integral representation of the Mathieu $\left(\textbf{a},\bm{\lambda}\right)$-series is rederived by applying the Abel's summation formula (which provides a slight modification of the result given by Pog\'{a}ny [Integral Transforms Spec. Funct. 16 (8) (2005) 685--689]) and this modified form of the result is then used to obtain a new integral representation for the $\lambda$-generalized Hurwitz-Lerch Zeta function. Finally, by making use of the various results presented in this paper, we establish two sets of two-sided inequalities for the $\lambda$-generalized Hurwitz-Lerch Zeta function.

This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7(2014), 168-179]. A new concept of (?-?1-?2)-contractive mapping using two altering distance functions in ordered b-metric-like space is introduced and basic fixed point results have been studied. Useful examples are illustrated to justify the applicability and effectiveness of the results presented herein. As an application, the existence of solution of fourth-order two-point boundary value problems is discussed and rationalized by a numerical example.

The purpose of this paper is to present some fixed point results in b-metric spaces using a contractive condition of Hardy-Rogers type with respect to the functional H. The data dependence of the fixed point set, the well-posedness of the fixed point problem, as well as, the Ulam-Hyres stability are also studied.

In this paper, the authors investigate a majorization problem for certain subclasses of multivalent meromorphic functions defined in the punctured unit disk U* having a pole of order p at origin. The subclasses under investigation are defined through iterations and combinations of the Liu-Srivastava operator and a meromorphic analogue of the Cho-Kwon-Srivastava operator for normalized analytic function. Several consequences of the main results in form of corollaries are also pointed out.

In this paper, we propose a method based on generating functions for constructing q-analogues of some discrete type positive linear operators (e.g., q-Lupas, q-Bernstein, q-Meyer-Konig and Zeller and ¨ q-Bleimann-Butzer-Hahn operators etc.). In other words, general operators of the discrete type are constructed, and their respective formulae for central moments are thereby obtained. Finally, through the use of specific generating functions, we are able to provide some relevant exemplary applications of general operators.

In this paper, inspired the very interesting results of Ciric [20], we investigate the existing non-unique fixed points of certain operators in the context of b-metric spaces. Our main results unify and cover several existing results on the topic in the literature.

The classical power sum and alternating power sum identities can be stated as ?m,i=0 sn(i)= 1/n+1 (Bn+1(m+1)- Bn+1), ?m,i=0(-1)i sn (i) = 1/2 ((-1)m En(m+1) + En), where sn(x)=xn is the simplest possible Appell polynomial for the Sheffer pair (1,t). The impetus for this research starts from the question that what if we replace sn(x)=xn by any Appell polynomial. In this paper, we give a generalization of power and alternating power sums to any Appell polynomials.

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, the concept of (?-?)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi bmetric spaces is obtained. Some examples are presented to show that the results proved herein are potential generalization and extension of comparable existing results in the literature. We also study Ulam-Hyers stability of fixed point problems of (?-?)-generalized rational contraction multivalued operator. We also obtain some common fixed point results for single and multivalued mappings in a complete dq b-metric space endowed with a partial order. As an application, the existence of a continuous solution of an integral equation under appropriate assumptions is obtained.

The aim of this paper is to further investigate properties of the local closure function, as a generalization of the ?-closure and the local function in ideal topological spaces. Similarities and differences between it and the local function are examined by varying several well-known ideals.

We introduce the concept of a soft ditopological space as the "soft Generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Ert?rk, ?. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147 (2) (2004), 171-199. Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology. The first one is used to describe openness-type properties of a space while the second one deals with its closedness-type properties. We study basic properties of such spaces and accordingly defined continuous mappings between such spaces.

In this paper we study fuzzy hyperideals of a fuzzy hyperring, we define and analyze two particular kinds of fuzzy hyperideals, which extend similar notions of ring context, namely prime fuzzy hyperideals and maximal fuzzy hyperideals. Moreover, we study the hyperideal transfer through a fuzzy hyperring homomorphism, particularly for prime fuzzy hyperideals and for maximal fuzzy hyperideals.

In this paper we give a generalization of the Lagrange mean value theorem via lower and upper derivative, as well as appropriate criteria of monotonicity and convexity for arbitrary function f : (a, b) ( R. Some applications to the neoclassical economic growth model are given (from mathematical point of view).