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Super Metric Spaces are a ground-breaking generalization of metric spaces that were recently developed by Karapinar and Khojasteh (Filomat, in press). In this paper, we initiate the study of expansive fixed points in the context of the supermetric spaces. Our results may open the door to more expansive fixed point results in a different direction. [ABSTRACT FROM AUTHOR]

In this article, we prove a new compactness criterion in the Lebesgue spaces Lp(ℝ+), 1 ≤ p < ∞ and use such criteria to construct a measure of noncompactness in the mentioned spaces. The conjunction of that measure with the Hausdroff measure of noncompactness is proved on sets that are compact in finite measure. We apply such measure with a modified version of Darbo fixed point theorem in proving the existence of monotonic integrable solutions for a product of n-Hammerstein integral equations n ≥ 2. [ABSTRACT FROM AUTHOR]

In this paper, we define θ-expansions on Branciari metric spaces by complementing the concept of θ-contractions introduced by Jleli and Samet (J. Inequal. Appl. 2014:38, 2014). Also, we present some new fixed point results for θ-expansion mappings on a Branciari metric space. [ABSTRACT FROM AUTHOR]

In this paper, we define a generalized resolvent operator involving a 풢 ⁢ (⋅ , ⋅) -co-monotone mapping for solving a generalized variational inclusion problem. We show that the resolvent operator under consideration is single-valued as well as Lipschitz continuous. An iterative algorithm is constructed to obtain the approximate solution of our problem. An example is provided to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

In the current paper a new form of Durrmeyer-type operator involving the beta function is introduced and its approximation properties are studied. We obtain the rate of convergence in different terms. Order of approximation for functions of some special class is also obtained. We establish the Voronovskaja type asymptotic result for this operator and the direct estimate. [ABSTRACT FROM AUTHOR]

This paper deals with the approximation properties of a generalized version of Szász–Mirakjan operators which preserve a x {a^{x}} , a > 1 {a>1} (fixed), and x ≥ 0 {x\geq 0}. The uniform convergence of the operators is studied by using some auxiliary results. Also, error estimations are determined by considering the functions from different spaces. The convergence of the said operators is shown and analyzed by graphics. In the same direction, the proposed operators are compared with Szász–Mirakjan operators for the rate of convergence. A Voronovskaya-type theorem is considered and a comparison with Szász–Mirakjan operators is shown in the sense of convexity. To describe the quantitative means of an asymptotic formula, we quantitatively approach the Voronovskaya-type theorem; moreover, a Grüss–Voronovskaya-type theorem is proved. For further investigations regarding the approximation for functions from various spaces, two significant extensions are added keeping in mind some developments in the L p {L_{p}} -space. One is the Kantorovich variant and the other one is the Durrmeyer modification of the defined operators. Here, the rate of convergence is described by means of the function with a derivative of bounded variation for the Durrmeyer modified operators for which some properties are discussed. Also, A-statistical properties of the Durrmeyer modified operators are established. This paper ends by presenting some significant statements and the conclusion. [ABSTRACT FROM AUTHOR]

In this paper, we introduce C*-algebra valued modular S-metric spaces. Some common fixed point results for S-weak operator pair on C*-algebra valued modular S-metric spaces is given with suitable examples. Stability of the fixed point and application for a system of integral equations are also discussed here. [ABSTRACT FROM AUTHOR]

The motive of this research article is to introduce a sequence of Sz$ \acute{a}sz $ Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation properties. Further, preliminaries results and definitions are presented. Moreover, we study existence of convergence with the aid of Korovkin theorem and order of approximation via usual modulus of continuity, Peetre's K-functional, Lipschitz maximal functional. Lastly, approximation properties of these sequences of operators are studied in B$ \ddot{o} $gel space via mixed modulus of continuity. [ABSTRACT FROM AUTHOR]

In the present paper, we discuss the approximation properties of Jain–Baskakov operators with parameter c. The paper deals with the modified forms of the Baskakov basis functions. Some direct results are established, which include the asymptotic formula, error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct the King modification of these operators, which preserves the test functions e 0 {e_{0}} and e 1 {e_{1}}. It is shown that these King type operators provide a better approximation order than some Baskakov–Durrmeyer operators for continuous functions defined on some closed intervals. [ABSTRACT FROM AUTHOR]

Dynamics of composition of entire functions is well related to its factors, as it is known that for entire functions ƒ and g, ƒog has wandering domain if and only if goƒ has wandering domain. However the Fatou components may have different structures and properties. In this paper we have shown the existence of domains with all possibilities of wandering and periodic in given angular region θ. [ABSTRACT FROM AUTHOR]

In this manuscript, we focus on the approximation of fixed points for multivalued nonexpansive type mappings within uniformly convex Banach spaces. To achieve this goal, we utilize a three-step iteration scheme that was originally introduced by Ullah et al. Furthermore, we establish the rapid convergence properties of the Ullah et al. iteration scheme through the implementation of numerical examples using Matlab software. [ABSTRACT FROM AUTHOR]

The motivation behind this article is to study a class of nondifferentiable multiobjective fractional programming problem in which each component of objective functions contains a term including the support function of a compact convex set. For a differentiable function, we consider a class of higher order pseudo quasi/ strictly pseudo quasi/weak strictly pseudo quasi- (V, p, d)-type-I convex functions. Under these the higher-order pseudo quasi/ strictly pseudo quasi/weak strictly pseudo quasi- (V, p, d)-type-I convexity assumptions, we prove the higher-order weak, higher-order strong and higher-order converse duality theorems related to efficient solution. establish Jensen-type and Hermite-Hadamard-type inequalities. [ABSTRACT FROM AUTHOR]

Levels of fast escaping sets were discussed by Rippon and Stallard. Here we have defined a set BR(f) analogous to 0th level of fast escaping set by using maximum term and formation of spider's web structure has been discussed for this set. [ABSTRACT FROM AUTHOR]

In this paper we investigate a new (α , β) {(\alpha,\beta)} -metric F = β + a ⁢ α 2 + β 2 α {F=\beta+\frac{a\alpha^{2}+\beta^{2}}{\alpha}} , where α = a i ⁢ j ⁢ y i ⁢ y j {\alpha=\sqrt{{a_{ij}y^{i}y^{j}}}} is a Riemannian metric; β = b i ⁢ y i {\beta=b_{i}y^{i}} is a 1-form and a ∈ (1 4 , + ∞) {a\in(\frac{1}{4},+\infty)} is a real scalar. Also, we investigate the relationship between the geodesic coefficients of the metric F and the corresponding geodesic coefficients of the metric α. [ABSTRACT FROM AUTHOR]

In the present paper, we discuss the approximation properties of Durrmeyer-Stancu type variant of Jain operators with the modified forms of the Beta basis functions. We establish some direct results, which include the asymptotic formula, the error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct a King modification of these operators which preserves the test functions e0 and e1. [ABSTRACT FROM AUTHOR]

In this paper, we first study a composite relaxed resolvent operator and prove some of its properties. After that, we introduce a Yosida approximation operator based on the composite relaxed resolvent operator and demonstrate some properties of the Yosida approximation operator. Finally, we obtain the solution of a system of Yosida inclusions by applying these concepts. We construct a conjoin example in support of many concepts derived in this paper. Our concepts and results are new in the literature and can be used for further research. [ABSTRACT FROM AUTHOR]

The extension of the exponential function is the Mittag-Leffler function. In physical implications, the MittagLeffler function is becoming more and more crucial, as a result a number of researchers are investigating different generalizations and extensions associated with the Mittag-Leffler function. In this present article, we define the bicomplex r-parameter Mittag-Leffler function which is an extension of bicomplex one parameter Mittag-Leffler function. In addition, various properties of this function like integral representation, differential relation, duplication formula, bicomplex C-R equation, analyticity, region of convergence, order and type are established. Additionally, the bicomplex r-parameter MittagLeffler function’s Laplace transform and Caputo fractional derivative are produced. [ABSTRACT FROM AUTHOR]

In this paper, the Szász-Mirakjan-Kantorovich type operators are studied with the help of direct result and weighted approximation properties. Some basic lemmas, theorems are given and proved, at last, we discuss the rate of convergence and a comparison takes place with the Szász-Mirakjan-Kantorovich operators by graphical representations. [ABSTRACT FROM AUTHOR]

Given a function f in the class Lip(α, p) (0 ≤ α 6 1, p ≥ 1), Mittal and Singh (2014) approximated such an f by using trigonometric polynomials, which are the nth terms of either certain Riesz mean or Nörlund mean transforms of the Fourier series representation for f. They showed that the degree of approximation is O((λ(n))-α) and extended two theorems of Leindler (2005) where he had weakened the conditions on {pn} given by Chandra (2002) to more general classes of triangular matrix methods. We obtain the same degree of approximation for a more general class of lower triangular matrices. [ABSTRACT FROM AUTHOR]

The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and A-statistical convergence are established. Our results are based on a ρ function. These results include the preservation properties of the classical Baskakov operators. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain local approximation results for Stancu type generalization of modified Szász-Mirakjan operators. First, we calculate moments of the operators. Some direct results of the operators are investigated. The rate of convergence of the operators is evaluated. In last section of the paper, the Voronovskaya type result is obtained. [ABSTRACT FROM AUTHOR]

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study 3-dimensional β- Kenmotsu manifolds whose metric is Ricci soliton with respect to Schouten- van Kampen connection. We found the condition for the Ricci soliton structure to be invariant under Schouten-van Kampen connection. We have also showed that the Ricci soliton structure with respect to usual Levi-Civita connection transforms to a η-Ricci soliton structure under D-homothetic deformation. Finally we have shown that if a 3-dimensional β-Kenmotsu manifold admits a Ricci soliton structure with respect to Schouten-van Kampen connection and potential vector field as the Reeb vector field, then the manifold becomes K -contact Einstein. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Stancu variant of generalized (p; q)-Szász-Mirakyan operators. Initially, we estimate moments of the operators. Using Korovkin’s result, we have evaluated the uniform convergence of the operators. Direct results of the operators have been appraised. For better approximation we have calculated the rate of convergence of the operators. Last, we have proved Voronovskaya type theorem for the operators. Particularly, if α = 0 then we get the generalized (p; q)-Szász-Mirakyan operators. [ABSTRACT FROM AUTHOR]

Theory of approximation is a very extensive field and study of approximation via qcalculus and (p, q)- calculus is of great mathematical interest with great practical importance. Positive approximation processes play an important role in approximation theory and appear in a very natural way dealing with approximation of continuous functions, especially one, which requires further qualitative properties such as monotonicity, convexity and shape preservation and so on. This paper deals with the q-form of Dunkl generalization of Szász - Beta type operators. Estimation of their moments and establishing basic approximation results which comprise weighted approximation and direct estimates in view of modulus of continuity is the aim of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Stancu type generalization of modified Srivastava-Gupta operators. We obtain the moments of the operators and then prove the basic convergence theorem. Next, the Voronovskaja type asymptotic formula and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimates using the Lipschitz type maximal function and two parameter Lipschitz-type space. Further, we study the A-statistical convergence of these operators. Lastly, we give better estimations of the above operators using King type approach. [ABSTRACT FROM AUTHOR]

The Voronovskaja type asymptotic formula for function having q- derivative of the integral generalization Bernstein operators based on q-integer is discussed. The same formula for Stancu type generalization of this operators is mentioned. [ABSTRACT FROM AUTHOR]

In this article a new result on |A; pm; qn; δ|k summability of doubly infinite lower triangular matrix has been establised which generalizes a theorem of E. Savas and B.E. Rhoades and subsequently a theorem of Paikray et al. on summability factor of double infinite weighted mean matrix. [ABSTRACT FROM AUTHOR]

In this paper, utilizing the technique of generalized Darbo's fixed‐point theorem associated with measure of noncompactness in Banach space, we analyze the existence of solution for a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator. The existing result was obtained to strengthen the ones mentioned previously in the literature. An example for a class of nonlinear functional integral equations is also presented to validate our main result. Finally, we propose the numerical method formed by the modified homotopy perturbation approach to resolving the problem with acceptable accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we study a natural modification of Szász-Mirakjan operators. It is shown by discussing many important established results for Szász-Mirakjan operators. The results do hold for this modification as well, be they local in nature or global, be they qualitative or quantitative. It is also shown that this generalization is meaningful by means of examples and graphical representations. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this work, we investigate weighted αβ-statistical approximation properties of q-Durrmeyer-Stancu operators. We also give some corrections in limit of q-Durrmeyer-Stancu operators defined in [1] and discuss their convergence properties. [ABSTRACT FROM AUTHOR]

In the present paper, we study the mixed summation integral type operators having Baskakov and Szász basis functions in summation and integration form, respectively. We also give here the alternate form of the operators in terms of hypergeometric functions and estimated moments of these operators using hypergeometric series. In the last section, we present some results for operators related to convergence. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a summation-integral type modification of Szász-Mirakjan operators. Calculation of moments, density in some space, a direct result and a Voronvskaja-type result, are obtained. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we have proved the degree of approximation of functions belonging to L[0, ∞) by Harmonic-Euler means of its Fourier-Laguerre series at x = 0. The aim of this paper is to concentrate on the approximation properties of the functions in L[0, ∞) by Harmonic-Euler means of its Fourier-Laguerre series associated with the function f. [ABSTRACT FROM AUTHOR]

In this paper we have established interesting results involving continued fraction. Special cases of the result established herein have also been discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalization of the Kantorovich-type Bernstein operators based on q-integers and get a Bohman-Korovkin-type approximation theorem of these operators. We also compute the rate of convergence using the first modulus of smoothness. [ABSTRACT FROM AUTHOR]

In this paper, a kind of modified Baskakov–Schurer–Szász operators (1.2) is introduced. Approximation properties of theses operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the convergence in certain weighted spaces is investigated. Furthermore, we study q -analogues of Baskakov–Schurer–Szász operators and its Stancu generalization. Then the better error estimations for the operators (6.3) by using King type approach is investigated. In the last section the Korovkin type weighted statistical approximation property of operators (9.1) is given. [ABSTRACT FROM AUTHOR]

We introduce certain modified Szász-Mirakyan operators in polynomial weighted spaces of functions of one variable. We studied approximation properties of these operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the q-analogue of Baskakov-Szász-Stancu operators. First, we use properties of q-calculus to estimate moments of these operators. We have estimated some approximation properties and asymptotic formula for these operators. In last section, we give better error estimations for said operators. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a simple integral generalization of q-analog of well known Bernstein operators with two parameters α and β, which was introduced in Mishra and Patel (2013) [17]. We give detail proof of the rate of convergence and Voronovskaja type asymptotic formula for the operators Dn, qα, β . Also, we establish statistical convergence for these operators and discuss modification of the operators Dn, qα, β for better approximation results over compact interval. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a modification of Szfisz operators involving generalized Brenke type polynomials, First, we investigate Korovkin's type approximation theorem, Next, we established an approximation result for the functions in Lipschitz type space, Furthermore, we discuss the rate of convergence by means of the Ditzian-Totik modulus of smoothness, Lastly, we established an approximation result for the functions having derivatives of bounded variation. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, a new theorem on the degree of approximation of function conjugate to a 2π periodic function f belonging to the generalized weighted Lipschitz -class by dropping the monotonicity condition on the generating sequence {pn } has been established which in turn generalizes the results of Lal (2009) [12] on Fourier series. We also note some errors appearing in the paper of Lal (2009) [12] and rectify them in the view of observations of Rhoades et al. (2011) [22]. [Copyright &y& Elsevier]