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Artion Kashuri and Rozana Liko

Abstract

In this article, we first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-(r; m; h)-preinvex mappings. And then, a new identity concerning twice differentiable mappings defined on m-invex set is derived. By using the notion of generalized relative semi-(r; m; h)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard, Ostrowski and Simpson type inequalities via fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

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S. Sümer Eker and Bilal Şeker

Abstract

In this paper, defining new interesting classes, λ-pseudo bi-starlike functions with respect to symmetrical points and λ-pseudo bi-convex functions with respect to symmetrical points in the open unit disk U, we obtain upper bounds for the initial coefficients of functions belonging to these new classes.

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Alok Kumar and Vandana

Abstract

In this paper we introduce and study the Stancu type generalization of the integral type operators defined in (1.1). First, we obtain the moments of the operators and then prove the Voronovskaja type asymptotic theorem and basic convergence theorem. Next, the rate of convergence and weighted approximation for the above operators are discussed. Then, weighted Lp-approximation and pointwise estimates are studied. Further, we study the A-statistical convergence of these operators. Lastly, we give better estimations of the above operators using King type approach.

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Farrukh Jamal, Mohammad A. Aljarrah, M. H. Tahir and M. Arslan Nasir

Abstract

In this paper, we introduce a new extended generalized Burr III family of distributions in the so- called T-Burr III {Y} family by using the quantile functions of a few popular distributions. We derive the general mathematical properties of this extended family including explicit expressions for the quantile function, Shannon entropy, moments and mean deviations. Three new Burr III sub-families are then investigated, and four new extended Burr III models are discussed. The density of Burr III extended distributions can be symmetric, left-skewed, right-skewed or reversed-J shaped, and the hazard rate shapes can be increasing, decreasing, bathtub and upside-down bathtub. The potentiality of the newly generated distributions is demonstrated through applications to censored and complete data sets.

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A. M. A. El-Sayed and M. M. A. Al-Fadel

Abstract

We present an existence theorem for at least one continuous solution for a coupled system of nonlinear functional (delay) integral equations of Urysohn-Stieltjes type.

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Abasalt Bodaghi and Pasupathi Narasimman

Abstract

In this paper, we introduce and obtain the general solution of a new generalized mixed quadratic and quartic functional equation and investigate its stability in non-Archimedean L-fuzzy normed spaces.

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Sunil K. Sharma, Kuldip Raj and Ajay K. Sharma

Abstract

In the present paper we introduce some sequence spaces combining lacunary sequence, invariant means over n-normed spaces defined by Musielak-Orlicz function ℳ= (Mk). We study some topological properties and also prove some inclusion results between these spaces.

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Harina P. Waghamore

Abstract

In this paper, we investigate the distribution of zeros as well as the uniqueness problems of certain type of differential polynomials sharing a small function with finite weight. The result obtained improves and generalizes the recent results.

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Marcelo Fiore

Abstract

We consider discrete enriched abstract clones and provide two constructions investigating their representation as discrete enriched clones of operations on objects in concrete enriched categories over the enriching category. Our first construction embeds a discrete enriched abstract clone into the concrete discrete enriched clone of operations on an object in the enriching category. Our second construction refines the given embedding by introducing a monoid action and restricting attention to the concrete discrete enriched clone of its equivariant operations. As in the classical theory of abstract clones, our main focus is on discrete enriched abstract clones with finite arities. However, we also consider discrete enriched abstract clones with countable arities to show that the representation theory of the former is conceptually explained by that of the latter.

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Farrukh Jamal, M. H. Tahir, Morad Alizadeh and M. A. Nasir

Abstract

Generalizing distributions is important for applied statisticians and recent literature has suggested several ways of extending well-known distributions. We propose a new class of distributions called the Marshall-Olkin Burr X family, which yields exible shapes for its density such as symmetrical, left-skewed, right-skewed and reversed-J shaped, and can have increasing, decreasing,constant, bathtub and upside-down bathtub hazard rates shaped. Some of its structural properties including quantile and generating functions, ordinary and incomplete moments, and mean deviations are obtained. One special model of this family, the Marshall- Olkin-Burr-Lomax distribution, is investigated in details. We also derive the density of the order statistics. The model parameters are estimated by the maximum likelihood method. For illustrative purposes, three applications to real life data are presented.