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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).

‎In this ‎paper,‎ we study two-stage stochastic linear ‎programming‎ ‎(‎SLP) ‎problems with fixed ‎recourse‎. The problem is often large scale as the objective function involves an expectation over a discrete set of scenarios. This paper presents a ‎parallel ‎implementation ‎of ‎the ‎augmented Lagrangian ‎method ‎for ‎solving ‎SLPs.‎ ‎‎‎‎‎‎‎‎‎‎Our parallel method is based on a modified version of the L-shaped method and reducing linear master and recourse programs to unconstrained‎ maximization of concave differentiable piecewise quadratic functions‎. ‎The maximization problem is solved using the generalized Newton method‎. ‎The parallel method is implemented in ‎Matl‎ab‎. ‎Large scale SLP with several millions of variables and several hundreds of‎ ‎thousands of constraints ‎a‎re solved‎. ‎The ‎‎results of uniprocessor and multiprocessor computations are‎ ‎presented ‎which‎‎‎ show that the parallel algorithm is ‎effective.‎

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 the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, 31 (2017), 3875-3884), we obtain the results of Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145-1163] with very much weaker conditions. Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value system for our 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.

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.

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.

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 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 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 this paper, we recall the notion of intuitionistic fuzzy 2- normed space introduced by Mursaleen and Lohani \cite { muri } and using the direct method, we investigate the Hyers Ulam - Rassias stability of the following quadratic functional equation \begin {equation*} \ label{main} f(ax+by)+f(ax-by)-\frac{a}{2}f(x+y)=\frac{a}{2}f(x-y)-(2a^{2}-a)f(x)-(2b^{2}-a)f(y) \end {equation*} in this space.

Lagrange multiplier method based o modified Lagrangian functionals is one of the main methods for solving the finite dimensional convex optimization problem. Recently the Lagrange multiplier method is successfully applied to the solution of infinite- dimensional variational inequalities in mechanics. Convergence of Lagrange multiplier method is provided with the help of property of lower semicontinuity of sensitivity function. It is possible to prove the continuous differentiability of dual function. It allows for the solution of a dual problem to apply effective gradient methods of maximizing. In our paper we investigate the Lagrange multiplier method in finite-dimensional convex optimization problem and in infinite-dimensional semicoercive Signorini's problem of mechanics.