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13 pages, 292 KiB

Open AccessArticle

An Application of Urysohn Integral Equation via Complex Partial Metric Space

by Rajagopalan Ramaswamy, Gunaseelan Mani, Arul Joseph Gnanaprakasam, Ola A. Ashour Abdelnaby and Stojan Radenović

Mathematics 2022, 10(12), 2019; https://doi.org/10.3390/math10122019 - 11 Jun 2022

Cited by 4 | Viewed by 1635

Abstract

Metric fixed point theory has vast applications in various domain areas, as it helps in finding analytical solutions under various contractive conditions, including non-linear integral-type contractions. In our present work, we have established fixed point results in the setting of complex valued partial [...] Read more.

Metric fixed point theory has vast applications in various domain areas, as it helps in finding analytical solutions under various contractive conditions, including non-linear integral-type contractions. In our present work, we have established fixed point results in the setting of complex valued partial metric space. Our results extend the results proven in literature. Using our main result, we have provided an application to find the solution to the Urysohn-type integral equation. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

10 pages, 335 KiB

Open AccessArticle

A New Kantorovich-Type Rational Operator and Inequalities for Its Approximation

by Esma Yıldız Özkan

Mathematics 2022, 10(12), 1982; https://doi.org/10.3390/math10121982 - 8 Jun 2022

Cited by 2 | Viewed by 1460

Abstract

We introduce a new Kantorovich-type rational operator. We investigate inequalities estimating its rates of convergence in view of the modulus of continuity and the Lipschitz-type functions. Moreover, we present graphical comparisons exemplifying concretely its better approximation for a certain function. The results of [...] Read more.

We introduce a new Kantorovich-type rational operator. We investigate inequalities estimating its rates of convergence in view of the modulus of continuity and the Lipschitz-type functions. Moreover, we present graphical comparisons exemplifying concretely its better approximation for a certain function. The results of the paper are crucial by means of possessing at least better approximation results than an existing Kantorovich-type rational function. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

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20 pages, 355 KiB

Open AccessArticle

Some New Beesack–Wirtinger-Type Inequalities Pertaining to Different Kinds of Convex Functions

by Artion Kashuri, Muhammad Samraiz, Gauhar Rahman and Zareen A. Khan

Mathematics 2022, 10(5), 757; https://doi.org/10.3390/math10050757 - 27 Feb 2022

Cited by 3 | Viewed by 1832

Abstract

In this paper, the authors established several new inequalities of the Beesack–Wirtinger type for different kinds of differentiable convex functions. Furthermore, we generalized our results for functions that are n-times differentiable convex. Finally, many interesting Ostrowski- and Chebyshev-type inequalities are given as [...] Read more.

In this paper, the authors established several new inequalities of the Beesack–Wirtinger type for different kinds of differentiable convex functions. Furthermore, we generalized our results for functions that are n-times differentiable convex. Finally, many interesting Ostrowski- and Chebyshev-type inequalities are given as well. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

18 pages, 319 KiB

Open AccessArticle

Refinement of Discrete Lah–Ribarič Inequality and Applications on Csiszár Divergence

by Đilda Pečarić, Josip Pečarić and Jurica Perić

Mathematics 2022, 10(5), 755; https://doi.org/10.3390/math10050755 - 26 Feb 2022

Viewed by 1422

Abstract

In this paper we give a new refinement of the Lah–Ribarič inequality and, using the same technique, we give a refinement of the Jensen inequality. Using these results, a refinement of the discrete Hölder inequality and a refinement of some inequalities for discrete [...] Read more.

In this paper we give a new refinement of the Lah–Ribarič inequality and, using the same technique, we give a refinement of the Jensen inequality. Using these results, a refinement of the discrete Hölder inequality and a refinement of some inequalities for discrete weighted power means and discrete weighted quasi-arithmetic means are obtained. We also give applications in the information theory; namely, we give some interesting estimations for the discrete Csiszár divergence and for its important special cases. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

10 pages, 257 KiB

Open AccessArticle

Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application

by Sanja Kovač and Ana Vukelić

Mathematics 2022, 10(5), 735; https://doi.org/10.3390/math10050735 - 25 Feb 2022

Cited by 3 | Viewed by 1623

Abstract

Recently, there have been many proven results of the Ostrowski–Grüss-type inequality regarding the error bounds for the Chebyshev functional when the functions or their derivatives belong to

L_{p}

spaces. In the existing literature, the main assumption in the weight-type results is that [...] Read more.

Recently, there have been many proven results of the Ostrowski–Grüss-type inequality regarding the error bounds for the Chebyshev functional when the functions or their derivatives belong to

L_{p}

spaces. In the existing literature, the main assumption in the weight-type results is that the derivative of the function is bounded by two constant functions. The aim of our paper is to extend those results in a way that the derivative of the function is bounded by two functions in

L_{p}

spaces. Furthermore, we give some new error estimations of the Chebyshev functional and applications to the one-point weight integral formulas. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

21 pages, 799 KiB

Open AccessArticle

Novel Generalized Proportional Fractional Integral Inequalities on Probabilistic Random Variables and Their Applications

by Weerawat Sudsutad, Nantapat Jarasthitikulchai, Chatthai Thaiprayoon, Jutarat Kongson and Jehad Alzabut

Mathematics 2022, 10(4), 573; https://doi.org/10.3390/math10040573 - 12 Feb 2022

Cited by 2 | Viewed by 1579

Abstract

This study investigates a variety of novel estimations involving the expectation, variance, and moment functions of continuous random variables by applying a generalized proportional fractional integral operator. Additionally, a continuous random variable with a probability density function is presented in context of the [...] Read more.

This study investigates a variety of novel estimations involving the expectation, variance, and moment functions of continuous random variables by applying a generalized proportional fractional integral operator. Additionally, a continuous random variable with a probability density function is presented in context of the proportional Riemann–Liouville fractional integral operator. We establish some interesting results of the proportional fractional expectation, variance, and moment functions. In addition, constructive examples are provided to support our conclusions. Meanwhile, we discuss a few specific examples that may be extrapolated from our primary results. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

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14 pages, 270 KiB

Open AccessArticle

Generalizations of Hardy Type Inequalities by Abel–Gontscharoff’s Interpolating Polynomial

by Kristina Krulić Himmelreich, Josip Pečarić, Dora Pokaz and Marjan Praljak

Mathematics 2021, 9(15), 1724; https://doi.org/10.3390/math9151724 - 22 Jul 2021

Cited by 6 | Viewed by 2168 | Correction

Abstract

In this paper, we extend Hardy’s type inequalities to convex functions of higher order. Upper bounds for the generalized Hardy’s inequality are given with some applications. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

14 pages, 275 KiB

Open AccessArticle

Hermite–Hadamard–Fejér-Type Inequalities and Weighted Three-Point Quadrature Formulae

by Mihaela Ribičić Penava

Mathematics 2021, 9(15), 1720; https://doi.org/10.3390/math9151720 - 22 Jul 2021

Cited by 1 | Viewed by 1856

Abstract

The goal of this paper is to derive Hermite–Hadamard–Fejér-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and w-harmonic sequences of functions. In special cases, Hermite–Hadamard–Fejér-type estimates are derived for various classical quadrature formulae [...] Read more.

The goal of this paper is to derive Hermite–Hadamard–Fejér-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and w-harmonic sequences of functions. In special cases, Hermite–Hadamard–Fejér-type estimates are derived for various classical quadrature formulae such as the Gauss–Legendre three-point quadrature formula and the Gauss–Chebyshev three-point quadrature formula of the first and of the second kind. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

6 pages, 248 KiB

Open AccessArticle

One Concave-Convex Inequality and Its Consequences

by Julije Jakšetić

Mathematics 2021, 9(14), 1639; https://doi.org/10.3390/math9141639 - 12 Jul 2021

Cited by 1 | Viewed by 1729

Abstract

Our starting point is an integral inequality that involves convex, concave and monotonically increasing functions. We provide some interpretations of the inequality, in terms of both probability and terms of linear functionals, from which we further generate completely monotone functions and means. The [...] Read more.

Our starting point is an integral inequality that involves convex, concave and monotonically increasing functions. We provide some interpretations of the inequality, in terms of both probability and terms of linear functionals, from which we further generate completely monotone functions and means. The latter application is seen from the perspective of monotonicity and convexity. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

10 pages, 290 KiB

Open AccessArticle

New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces \({L_{\vec{p}}(\mathbb{R}^d)}\)

by Junjian Zhao, Wei-Shih Du and Yasong Chen

Mathematics 2021, 9(3), 227; https://doi.org/10.3390/math9030227 - 25 Jan 2021

Cited by 9 | Viewed by 2179

Abstract

In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces

L_{\vec{p}} (R^{d})

. We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and [...] Read more.

In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces

L_{\vec{p}} (R^{d})

. We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and a stability theorem to mixed-norm case in the setting of shift-invariant subspace of

L_{\vec{p}} (R^{d})

. Our new results unify and refine the existing results in the literature. Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

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1 pages, 146 KiB

Open AccessCorrection

Correction: Krulić Himmelreich et al. Generalizations of Hardy Type Inequalities by Abel–Gontscharoff’s Interpolating Polynomial. Mathematics 2021, 9, 1724

by Kristina Krulić Himmelreich, Josip Pečarić, Dora Pokaz and Marjan Praljak

Mathematics 2023, 11(7), 1609; https://doi.org/10.3390/math11071609 - 27 Mar 2023

Viewed by 792

Abstract

In the published publication [...] Full article

(This article belongs to the Special Issue Mathematical Inequalities with Applications)

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