arXiv subjects

Adem Kiliçman

Publications and source records attributed to Adem Kiliçman.

4 recordsLinked to original sources

arXiv2023

On q-statistical approximation of wavelets aided Kantorovich q-Baskakov operators

The aim of this research is to examine various statistical approximation properties with respect to Kantorovich \textit{\text{\texthtq}}-Baskakov operators using wavelets. We discuss and investigate a weighted statistical approximation employing a Bohman-Korovkin type theorem as well as a statistical rate of convergence applying a weighted modulus of smoothness $ω_{ρ_α}$ correlated with the space $B_{ρα}(\mathbb{R_{+}})$ and Lipschitz type maximal functions. Both topics are covered in the article.

math.GM↗

arXiv2022

Blending type Approximations by Kantorovich variant of $α$-Schurer operators

In the present manuscript, we present a new sequence of operators, $i.e.$, $α$-Bernstein-Schurer-Kantorovich operators depending on two parameters $α\in[0,1]$ and $ρ>0$ for one and two variables to approximate measurable functions on $[0: 1+q], q>0$. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections. Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of first and second order modulus of smoothness, Peetre's K-functional and weight functions for these sequences in different spaces of functions.

math.GM↗

arXiv2021

Generalized Fejér-Hermite-Hadamard type via generalized $(h-m)$-convexity on fractal sets and applications

In this article, we define a new class of convexity called generalized $(h-m)$-convexity, which generalizes $h$-convexity and $m$-convexity on fractal sets $\mathbb{R}^α$ $(0<α\leq 1)$. Some properties of this new class are discussed. Using local fractional integrals and generalized $(h-m)$-convexity, we generalized Hermite-Hadamard (H-H) and Fejér-Hermite-Hadamard (Fejér-H-H) types inequalities. We also obtained a new result of the Fejér-H-H type for the function whose derivative in absolute value is the generalized $(h-m)$-convexity on fractal sets. Some applications to random variables and numerical integrations are studied.

math.FA↗

arXiv2018

On Properties of Geodesic Semilocal E-Preinvex Functions

The authors define a class of functions on Riemannian manifolds, which is called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions and some of its properties are established. Furthermore, a nonlinear fractional multiobjective programming is considered, where the functions involved are geodesic E-$ η$-semidifferentiability, sufficient optimality conditions are obtained. A dual is formulated and duality results are proved using concepts of geodesic semilocal E-preinvex functions, geodesic pseudo-semilocal E-prinvex functions and geodesic quasi-semilocal E-preinvex functions.

math.DG↗